Has any of the data centers turned any profits they have made after subtracting the costs?
I'm pretty sure the answer is "no" and anybody claiming profit is cooking the books.
I've actually wondered about this a lot. Short answer is I don't know, but I doubt it yet.
I have some thoughts though:
1. Amazon built it's foundation for 9 years before it ever made a dollar in profit.
2. In business there is the concept called a Moat. It is some kind of barrier that makes it hard for new competitors to enter your space.
AI is a unique because it is much more hardware constrained than previous info tech.
One reason I think hyper-scalars are building beyond their current profit is to build a Moat. Gotta have the chips. Chips are a finite resource. There are only so many available and can only be manufactured so fast. That is a choke-point.
If I was a big smart Hyper-Scalar with deep pockets, I’d buy up every chip there was. I’d pay top dollar. I’d drive up the prices as much as I can. I’d build out data-centers way in excess of my immediate needs. That is where I’d store all the chips I bought that I don’t need yet.

I’d grind that for 9 years until I’ve crushed every little startup that could have threatened me. (Relax. I’d give them all new jobs with me.) Then I’ve cleared the battlefield of distractions and can focus on only a couple of near-peers. What I financed to build out before I needed it was the cheapest ammo I could have bought to kill my weaker rivals, because I know I will eventually get to use it and it will pay for itself. Since I am big with deep pockets, and can play a decade long game, I can crush my smaller competitors that can’t float that. And it is the most legal market manipulation you could hope for. It’s not against the law to buy chips.
Also there is the real chance of a chip shortage from some Taiwan geopolitical crisis next year. What if no more GPU were available for 5 years? Who would be laughing then?
Ironically, it is the Chinese that are trying to come to the rescue. Their “Distilled” models pack near the same punch but need way less resources. That gives the little guys a way to subvert the Moat and undercut the Leviathans. That would also mean the biggies over-bought more than they realize. The Chinese are attempting to disrupt the US AI landscape. The last thing they want is the field to consolidate to a few strong players. What they want are a bunch of smaller players endlessly fighting amoungst themselves with none of them able to get critical mass. While they poison the minds of our population with culture war social media psyop programming to get us to economically cut out own throats like Instagram-Manchurian-Candidates.