It's not that you can't put a server in space, but the costs to do it almost assuredly don't make any sense. Because, if you can do it in space you can do it easier on the ground and save yourself millions in launch cost and extra complexity. Your cooling challenges are way cheaper and simpler in an atmosphere.

There's nothing much being in space really gets you, other than it makes it harder for a government to take your computers away. Not impossible, just harder.