Allow me to propose a modest alternative to space data centers, namely mountaintop data centers. This would consist of a container full of servers and GPUs and what else goes into a data center, a wind turbine for power and a communication module (say laser or microwave) for communicating with a base station with a fiber connection. This would be lifted on top of a mountain by a helicopter and bolted in place. Cooling would be provided by heat sinks exposed to the outside air. Some of the nodes could relay traffic from other nodes on remote mountain tops out of sight of the base station.
This scheme has many advantages over space data centers including launch costs, cooling, connection latency, servicability and ease of recycling.
A better idea is to put them on Mars, so people actually think before they send a stupid question.
What about the rough weather and difficulty of maintenance, especially in rough weather?
What advantage does a mountaintop have versus a more accessible earth-based location?
I suspect one of the motivations for space datacenters is to try to stay out of the reach of all jurisdictions so you Musk can start to run his companies as an autonomous state.
What would be accomplished by doing this vs placing them basically anywhere else on earth?
I think we can't rule out the explanation that all the ideas of space data centers could be connected to a desire by some of finding additional applications for rockets that can transport stuff to space.