One of the issues with putting servers in orbit is cooling; you can't just use fans in space. On the other hand, real estate is pretty cheap. Servicing is hard, though, and micrometeorites are another risk. Plus launch costs being high, and radiation an issue, I don't see it happening any time soon outside of very specific areas.
Radiation cooling is pretty dramatic in space. With an isolated radiation shield/mirror from the sun and a decent sized heatsink, you can have a lot of cooling power on hand. A server isn't going to be pumping out nearly as much heat as a rocket engine, and launch vehicles don't tend to overheat.
Forget cooling for a minute. Cooling dissipates energy but you need to collect the energy first and worry about powering the server. Itβs going to be a solar-plus-battery system, which is heavy and expensive, with substantial launch costs.
