yes. not entirely impossible, but highly impractical in the context of "datacenter in space".

releasing heat in space is quite tricky, since radiating it into vacuum is not very effective and datacenter generates enormous amount of it. it is basically heat factory.

i am imagining some borg cube datacenter surrounded by field of heat radiators god knows how long, some sort of datacenter-space-urchin.

might look cool as an illustration in scifi story, but that is where it will stay for a long time.