Manually Edit the Configuration File

Open the file /etc/apt/apt.conf by pressing Alt+F2 and running gksu gedit /etc/apt/apt.conf. Don't worry if it is an empty file. Add these lines into the file and save it:

Acquire::ftp::proxy "ftp://Username:Your_password@domain:port-no/";
Acquire::socks::proxy "socks://Username:Your_password@domain:port-no/";
Acquire::http::proxy "http://Username:Your_password@domain:port-no/";
Acquire::https::proxy "https://Username:Your_password@domain:port-no/";

Replace username by the username assigned to you and the password by your password, domain by the domain of your proxy like 10.1.101.150, which is my college's proxy address and by the port no like 3128 or the one which you have, if you do have these parameters assigned to you, else leave out username and password and also the characters: : and @ upto domain.

To add proxy authentication parameters to other applications, have a look at this answer to a similar question.

Use the Easy GUI Utility

Another way to add this information is by going to System Settings → Network → Network Proxy then add your proxy settings and click on Apply Settings System-wide. This will add the proxy settings but you will have to add the user-name and password manually using the command-line method described above.

There's a bug filed for this issue: https://bugs.launchpad.net/bugs/1180297

The root cause is that Facebook redirects to an insecure HTTP page during the authentication process, and for security reasons we don't allow that. The same problem appeared in February, and then Facebook was quick to fix it in a few days. Now it seems it's taking longer, but I'm still hopeful.