Resolved : "E: Archive directory /var/cache/apt/archives/partial is missing."

First of all, to clean your cache just use this command:

sudo apt-get clean

This will avoid this kind of problems in the future.

Lets try to solve this by remaking the missing directory:

sudo mkdir -m755 /var/cache/apt/archives/partial

(https://answers.launchpad.net/ubuntu/+source/apt/+question/9470)