I think most of you will encounter with this kind of problem if you are using the previous version of Ubuntu.
W: Failed to fetch gzip:/var/lib/apt/lists/partial/us.archive.ubuntu.com_ubuntu_dists_natty_main_source_Sources Hash Sum mismatch,
E: Some index files failed to download. They have been ignored, or old ones used instead.
The solution is to remove the content of /var/lib/apt/lists
directory:
sudo rm /var/lib/apt/lists/*
then run:
sudo apt-get update
Credit to askubuntu.com