Can I mine Bitcoin from my Hosting server? I have dedicated server which I leased for 6 months (paid upfront for Good Deal) and I just sold my website after 4 months which doesn't include Hosting (just transferd domain name and website files)

Now, my Dedicated Server 2 x Quad Core Xeon L5630 Processor, (8 Core Total) free for next two months.

Can I do Bitcoin/Etherium mining, is it allowed and what tools can I use? 
(though I Never mine Bitcoin before)
Since it is a dedicated server, I doubt that the company that you are leasing it from would care. But ultimately to answer that question, you need to take a look at the Terms &amp; Conditions of the leasing company.

Assuming that you can and want to, there is no difference between a leased server and one sitting on your desk, the tools are all the same. (Ok that's simplifying it because obviously you need to connect to the leased server via VPN, etc., but the main point remains).

Since you are new to mining bitcoin, I would recommend getting it up and working on a PC that you have physical access to, even if it's not for serious mining, you would learn a lot about how it works. Once you have it working locally, then I would deal with getting it working on your leased server.

Have fun!