E: Some index files failed to download. They have been ignored, or old ones used instead.

Look at https://launchpad.net/~boost-latest/+archive/ubuntu/ppa/+packages and you will see that the boost-latest PPA that you have enabled does not contain software for Ubuntu trusty. You have to remove this PPA from your list of repositories to get rid of the error message.

Suggested steps forward:
Why don't you upgrade to Ubuntu 16.04 (with boost 1.58) or Ubuntu 18.04 (with boost 1.65)?
You have to be aware that support for Ubuntu 14.04 (trusty) will end in April 2019.
For the remaining life time of trusty, ppa:marutter/c2d4u seems to provide boost 1.55 (standard disclaimer for PPAs applies of course).

first of all, thank you Manfred,
I removed it as like this

http://ask.xmodulo.com/find-remove-obsolete-ppa-repositories-ubuntu.html

but I get another problem, the output:

W: Duplicate sources.list entry http://dl.google.com/linux/chrome/deb/ stable/main amd64 Packages (/var/lib/apt/lists/dl.google.com_linux_chrome_deb_dists_stable_main_binary-amd64_Packages)
W: Duplicate sources.list entry http://dl.google.com/linux/chrome/deb/ stable/main amd64 Packages (/var/lib/apt/lists/dl.google.com_linux_chrome_deb_dists_stable_main_binary-amd64_Packages)
W: Duplicate sources.list entry http://dl.google.com/linux/chrome/deb/ stable/main amd64 Packages (/var/lib/apt/lists/dl.google.com_linux_chrome_deb_dists_stable_main_binary-amd64_Packages)
W: You may want to run apt-get update to correct these problems

someone explain it here:
https://ubuntuforums.org/showthread.php?t=1930785

I searched in sources. list, but I can't get any line as shown above

In addition to the /etc/apt/sources.list configuration file, there can be additional files in the /etc/apt/sources.list.d/ directory.

What is the output of the command
find /etc/apt -name '*.list' -exec bash -c 'echo -e "\n$1\n"; cat -n "$1"' _ '{}' \;

the output ''find /etc/apt -name '*.list' -exec bash -c 'echo -e "\n$1\n"; cat -n "$1"' _ '{}' \;'' :

/etc/apt/sources.list

     1 # deb cdrom:[Ubuntu 14.04.5 LTS _Trusty Tahr_ - Release amd64 (20160803)]/ trusty main restricted
     2
     3 # See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to
     4 # newer versions of the distribution.
     5 deb http://kr.archive.ubuntu.com/ubuntu/ trusty main restricted
     6 deb-src http://kr.archive.ubuntu.com/ubuntu/ trusty main restricted
     7
     8 ## Major bug fix updates produced after the final release of the
     9 ## distribution.
    10 deb http://kr.archive.ubuntu.com/ubuntu/ trusty-updates main restricted
    11 deb-src http://kr.archive.ubuntu.com/ubuntu/ trusty-updates main restricted
    12
    13 ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
    14 ## team. Also, please note that software in universe WILL NOT receive any
    15 ## review or updates from the Ubuntu security team.
    16 deb http://kr.archive.ubuntu.com/ubuntu/ trusty universe
    17 deb-src http://kr.archive.ubuntu.com/ubuntu/ trusty universe
    18 deb http://kr.archive.ubuntu.com/ubuntu/ trusty-updates universe
    19 deb-src http://kr.archive.ubuntu.com/ubuntu/ trusty-updates universe
    20
    21 ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
    22 ## team, and may not be under a free licence. Please satisfy yourself as to
    23 ## your rights to use the software. Also, please note that software in
    24 ## multiverse WILL NOT receive any review or updates from the Ubuntu
    25 ## security team.
    26 deb http://kr.archive.ubuntu.com/ubuntu/ trusty multiverse
    27 deb-src http://kr.archive.ubuntu.com/ubuntu/ trusty multiverse
    28 deb http://kr.archive.ubuntu.com/ubuntu/ trusty-updates multiverse
    29 deb-src http://kr.archive.ubuntu.com/ubuntu/ trusty-updates multiverse
    30
    31 ## N.B. software from this repository may not have been tested as
    32 ## extensively as that contained in the main release, although it includes
    33 ## newer versions of some applications which may provide useful features.
    34 ## Also, please note that software in backports WILL NOT receive any review
    35 ## or updates from the Ubuntu security team.
    36 deb http://kr.archive.ubuntu.com/ubuntu/ trusty-backports main restricted universe multiverse
    37 deb-src http://kr.archive.ubuntu.com/ubuntu/ trusty-backports main restricted universe multiverse
    38
    39 deb http://security.ubuntu.com/ubuntu trusty-security main restricted
    40 deb-src http://security.ubuntu.com/ubuntu trusty-security main restricted
    41 deb http://security.ubuntu.com/ubuntu trusty-security universe
    42 deb-src http://security.ubuntu.com/ubuntu trusty-security universe
    43 deb http://security.ubuntu.com/ubuntu trusty-security multiverse
    44 deb-src http://security.ubuntu.com/ubuntu trusty-security multiverse
    45
    46 ## Uncomment the following two lines to add software from Canonical's
    47 ## 'partner' repository.
    48 ## This software is not part of Ubuntu, but is offered by Canonical and the
    49 ## respective vendors as a service to Ubuntu users.
    50 # deb http://archive.canonical.com/ubuntu trusty partner
    51 # deb-src http://archive.canonical.com/ubuntu trusty partner
    52
    53 ## This software is not part of Ubuntu, but is offered by third-party
    54 ## developers who want to ship their latest software.
    55 deb http://extras.ubuntu.com/ubuntu trusty main
    56 deb-src http://extras.ubuntu.com/ubuntu trusty main

/etc/apt/sources.list.d/ros-latest.list

     1 deb http://packages.ros.org/ros/ubuntu trusty main

/etc/apt/sources.list.d/mendeleydesktop.list

     1 # This file lists the repositories for Mendeley Desktop.
     2 #
     3 # These repositories should work with most recent Debian/Ubuntu-based Linux
     4 # distributions.
     5 #
     6 # If you have any problems with Mendeley's Debian/Ubuntu repositories,
     7 # you can let us know at http://feedback.mendeley.com
     8 #
     9 # The distribution name sets the release channel you want to use,
    10 # which can be either "stable" or "preview"
    11
    12 deb https://desktop-download.mendeley.com/download/apt stable main

/etc/apt/sources.list.d/boost-latest-ppa-trusty.list

     1 # deb-src http://ppa.launchpad.net/boost-latest/ppa/ubuntu trusty main
     2 # deb-src http://ppa.launchpad.net/boost-latest/ppa/ubuntu trusty main

/etc/apt/sources.list.d/george-edison55-cmake-3_x-trusty.list

     1 deb http://ppa.launchpad.net/george-edison55/cmake-3.x/ubuntu trusty main
     2 # deb-src http://ppa.launchpad.net/george-edison55/cmake-3.x/ubuntu trusty main
     3 # deb-src http://ppa.launchpad.net/george-edison55/cmake-3.x/ubuntu trusty main

/etc/apt/sources.list.d/google-chrome.list

     1 ### THIS FILE IS AUTOMATICALLY CONFIGURED ###
     2 # You may comment out this entry, but any other modifications may be lost.
     3 deb [arch=amd64] http://dl.google.com/linux/chrome/deb/ stable main

/etc/apt/sources.list.d/mc3man-trusty-media-trusty.list

     1 deb http://ppa.launchpad.net/mc3man/trusty-media/ubuntu trusty main
     2 # deb-src http://ppa.launchpad.net/mc3man/trusty-media/ubuntu trusty main

/etc/apt/sources.list.d/google-talkplugin.list

     1 ### THIS FILE IS AUTOMATICALLY CONFIGURED ###
     2 # You may comment out this entry, but any other modifications may be lost.
     3 deb http://dl.google.com/linux/talkplugin/deb/ stable main

/etc/apt/sources.list.d/google.list

     1 deb [arch=amd64] http://dl.google.com/linux/chrome/deb/ stable main
     2 deb [arch=amd64] http://dl.google.com/linux/chrome/deb/ stable main
     3 deb [arch=amd64] http://dl.google.com/linux/chrome/deb/ stable main

/etc/apt/sources.list.d/graphics-drivers-ppa-trusty.list

     1 deb http://ppa.launchpad.net/graphics-drivers/ppa/ubuntu trusty main
     2 # deb-src http://ppa.launchpad.net/graphics-drivers/ppa/ubuntu trusty main

/etc/apt/sources.list.d/multiverse.list

     1 deb http://archive.ubuntu.com/ubuntu trusty main restricted universe multiverse

Execute the command

sudo rm /etc/apt/sources.list.d/google.list

to remove the duplcates and try the command

sudo apt-get updare

again.

the problem fixed now
thank you so so so much Manfred

unfortunately, I can't update boost from 1.54 to 1.55, this one of caffe's Prerequisites

please help me

Have you tried the PPA ppa:marutter/c2d4u ?

As already written in a previous message, support for Ubuntu 14.04 will end next April. If you upgrade to Ubuntu bionic, you will find caffe and all its dependencies in the standard repositories.
Is there anything preventing an upgrade of your system now?

thank you so much, Manfred,
I update boost 1.54 to 1.55, then installed caffe finally
yes, indigo ROS is preventing an update system of a robot
also, I forced some problem when installing indigo after update boost

If you look at http://wiki.ros.org/Distributions you see that support for ROS Indigo will also end in April 2019 (together with the EOL date of Ubuntu 14.04).
You should consider an upgrade to Ubuntu 16.04 with ROS Kinetic or Lunar, or to Ubuntu 18.04 with ROS Melodic in due course.

thanks, Manfred, I know that my dear and I will update it in close future