cant install new packadges-low disk space

Hello all,
I have done some research here before post this. but I still could not understand why I am having the low disk space problem.
I will try to be as clear possible and will be grateful for your help.

I have a dual boot with windows 7 installed and Ubuntu.

I Created several partitions:
- 1* 255Mb -grub
- 1* 45G -windows
- 1* 8G -Ubuntu
- 1* 62G -shared files with windows/storage

Since I installed and partitioned Ubuntu i receive low disk warnings, and now I cant install any more packadges,
I already did in the terminal the procedure (df -h ; sudo apt-get clean ; sudo dpkg -l | grep -i linux-image) *The result is bellow.

It says I am using 96% of the /dev/sda8 (7G) BUT when I double click in my 8G Ubuntu partition says I am only using 127.8 Mb and have 7,2G free. I am really confused...! down bellow is the image from terminal and a print screen from my 8G partition.

Terminal:
nn@nn-Latitude-E6420:~$
nn@nn-Latitude-E6420:~$ df -h
Filesystem Size Used Avail Use% Mounted on
/dev/sda8 7.7G 7.0G 315M 96% /
none 4.0K 0 4.0K 0% /sys/fs/cgroup
udev 1.9G 4.0K 1.9G 1% /dev
tmpfs 384M 1.3M 382M 1% /run
none 5.0M 0 5.0M 0% /run/lock
none 1.9G 80K 1.9G 1% /run/shm
none 100M 40K 100M 1% /run/user
/dev/sda3 42G 40G 2.6G 94% /media/nn/0A72D73C72D72B69
/dev/sda6 7.3G 122M 6.8G 2% /media/nn/1f6ee704-b79d-4140-8a9a-f7fa6fe9838c
/dev/sda1 236M 52M 172M 23% /media/nn/1306e7ec-de32-43ab-bb52-97a240574cc5
/dev/sda7 58G 38G 21G 65% /media/nn/56D575C162295DAE
nn@nn-Latitude-E6420:~$ sudo apt-get clean
[sudo] password for nn:
nn@nn-Latitude-E6420:~$ sudo apt-get clean
nn@nn-Latitude-E6420:~$ sudo dpkg -l | grep -i linux-image
ii linux-image-3.16.0-30-generic 3.16.0-30.40~14.04.1 amd64 Linux kernel image for version 3.16.0 on 64 bit x86 SMP
ii linux-image-3.16.0-31-generic 3.16.0-31.43~14.04.1 amd64 Linux kernel image for version 3.16.0 on 64 bit x86 SMP
ii linux-image-extra-3.16.0-30-generic 3.16.0-30.40~14.04.1 amd64 Linux kernel extra modules for version 3.16.0 on 64 bit x86 SMP
ii linux-image-extra-3.16.0-31-generic 3.16.0-31.43~14.04.1 amd64 Linux kernel extra modules for version 3.16.0 on 64 bit x86 SMP
ii linux-image-generic-lts-utopic 3.16.0.31.24 amd64 Generic Linux kernel image
nn@nn-Latitude-E6420:~$

PRINT SCREEN image of partition size: (in this image in the left side you can also see my partitions in the launcher)
http://postimg.org/image/tv28rkuwr/

Can you please help me?
Thanks in advance.