If I had a server, but I don't want to have it at home, at all costs.

(dreaming starts here)
I'd like to put my server (size of a home PC) in a room that would be 1m by 1m by 2m. Which would have electricity slot (I don't know the name of it, the thing that you put your plug in). And that I would be able to buy internet connection at any provider and that this internet could arrive through internet cable (ethernet) to my room. And that I would pay fee for that room and electricity monthly, and then for ISP seperately of course.
(dreaming ends here)

Does such even exist? Is it even possible to find such organization or any instance that would allow this? If so, how is it called? I would like to Google this word up and find someplace nearby me.

Please, don't ask why I don't want to have it at home or at my garage, it's such a long pointless story.

Whoops, nevermind, found it: "Colocation centre".