How to clear apt cache (packages cache) in Debian and Ubuntu

Question: 

How to clear apt cache (packages cache) in Debian and Ubuntu

Answer: 

You can clear up some disk space in your Debian / Ubuntu Linux if you clear the apt cache.

Over time you might have acculumated many megabytes or even gigabytes of cached apt packages and it's a good idea to clean the cache directory from time to time. You can see how much disk space your apt cache has taken up by going to the directory /var/cache/apt

To clear the apt cache and free up some space simply run: 

sudo apt-get clean