by my calculations, the heat dissipation isn't that big a deal

take an h100 for example. it will need something like 1kW to operate. that's less than 4 square meters of solar panel

at 70C, a reasonable temp for H100, a 4 square meter radiator can emit north of 2kW of energy into deep space

seems to me like a 2x2x2 cube could house an H100 in space

perhaps I'm missing something?

Heat travels when there is a thermal gradient. What thermally superconducting material are you going to make your cube out of that the surface temperature is exactly the same as the core temperature? If you don't have one, then to keep the h100 at 70c, the radiators have to be colder. How much more radiator area do you need then?

Have you considered the effects of insolation? Sunlight heats things too.

How efficient is your power supply and how much waste heat is generated delivering 1kW you your h100?

How do you move data between the ground and your satellite? How much power does that take?

If it's in LEO, how many thermal cycles can your h100 survive? If it's not in LEO, go back to the previous question and add an order of magnitude.

I could go on, but honestly those details - while individually solvable - don't matter because there is no world where you would not be better off taking the exact same h100 and installing it somewhere on the ground instead

The typical GPU cloud machine will have 8 H100s in a box. I didnt check your math but if a single machine needs 32 square meter radiator, 200 machines will probably be the size comparable to the ISS.

How much does it cost to launch just the mass of something that big?

Do you see how unrealistic this is?

Given that budget, I can bundle in a SMR nuclear reactor and still have change left.