You just need ballons (5m) and a city (20m). Easy, right? Now imagine me phrasing that without sarcasm and really trying to sell you on it, while still never doing the actual math.
That is the problem here. The idea is one that is designed to appeal to a specific audience. It is not an idea that makes sense to anybody who runs data centers or builds satellites.
Let's talk physics: In space there is no air, that means fans are useless. That means the extremely cold outside temperature is absolutely useless for cooling, because it is essentially a vacuum. The kind of vacuum used by the thermos company to keep your tea warm. Only the tea is now a data center emitting megawatts of heat. If you don't want the datacenter to melt you will need to get heat out and in space you can only do that by passive radiation, which is essentially copper radiating heat out. We have the math to calculate how big that radiator needs to be to be able to move energy out, and to no surprise it is going to habe to be significantly bigger than any active cooling solution used in a data center (just like passive coolers in PCs have to be bigger to allow the same power dissipation). Now mind they estimated the cost for cooling with 0 USD. I don't know how much copper they are going to but with 0 USD, but either they haven't the slightest clue what they are doing or they try to trick you. Keeping the temperature of satelites stable is a major challenge and if I have heard that, they know that too. Keep in mind this is just cooling, there are other significant parts they skip entirely, like communications, maintenance, RND costs, massive amounts of radiators..
A data center in space is more than taking a satellite and a data center and mashing them together. There are specific challenges to operating a data center in space, some of which may make it so uneconomic that it doesn't make sense to do it, just like a floating city. It looks cool in the drawings tho.