There is no magic bullet for “move this massive amount of heat somewhere else”

Space does let you dissipate heat via radiation (just not convection or conduction). Space radiators are a well understood and often-used technology.

The problem with space data centers isn’t the technology, we have the technology. It’s the cost. Everything in space is orders of magnitude more expensive than terrestrially. It’s simply not economically feasible to build a data center in space when you can build hundreds for the same cost on Earth.