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.
No you can't just build and build there are planning laws and you know other structures in the way. Space allows for effectively infinite expansion. In theory you could build a structure billions of kilometers across obviously you would never actually do that but the point is you could so it's effectively infinite.
If you try building a 20 km building on Earth people are going to get mad at you and also you need to buy land which kind of gets expensive assuming the land is even available which often it won't be assuming it's even stable enough to construct on which often it won't be.