An average rocket launch for SpaceX costs 74 million. A business they break even on. Let's assume they get a bit more efficient and they get that down to 70 million per launch. According to Elon Musk's own estimate, the space data center will be 150 KW, roughly one Nvidia AI rack. It probably has to be under volted a bit and run at 120 - 140 kw, but, whatever, roughly equivalent.
A 100 MW data center costs up to 5 billion and to power it costs roughly 150 million a year, so let's just say 1 billion more for five years of power, so 6 billion dollars for the first 5 years of the data center's operation. Why just 5 years? Because that is how long a Starlink low-earth orbit satellite stays up before it is scuttled and burns up in Earth's atmosphere, so after 5 years you can write that thing off.
Anyway, the benchmark is set. 100 MW data center at 6 billion dollars. But hey, there are roadblocks here on earth; land isn't cheap and costs keep going up, so let's worst case scenario this and say the cost of a terrestrial data center doubles to 10 billion dollars and power costs quadruple. So that's a worst case scenario baseline cost of an astonishing 14 billion dollars for a terrestrial 100 MW data center with power for five years.
70 million per rocket launch seems like pennies compared to 14 billion dollars and power is free in space! But wait, you would of course need 666 of these 150 KW mini data centers to be equivalent to one 100 MW data center. So, 666 SpaceX rocket launches, at 70 million dollars per, equals 46+ billion dollars. And that is before you factor in any other, you know, data center costs.
So no, there is no life time where it is cheaper to have data centers in space, but it may be a thing Elon does just to keep the stock price high.