In practice these models are typically run using top-tier A100 GPUs, which apparently is the cheapest thing you can do at scale: https://forum.effectivealtruism.org/posts/foptmf8C25TzJuit6/.... It looks like you can get away with just $10/hour, but I'm not sure I believe it. In one hour you can roughly generate 6 million English words this way, that's quite cheap.
But if you want to own the full hardware, then it's quite more expensive. You need 8 of those A100 GPUs, which come at $32k a piece, so you're in the ballpark of > $300k to build the server you need. Then there's of course running costs, these GPUs burn 250W a piece, plus the rest of the server we're at about 3kW power. That's not much, maybe $0.50/hr, plus maybe another $1/hr to cool the room it's in, depending on where it is (and the season, I guess in winter a fan might suffice, it's about as powerful as a couple small electric heaters). So with an upfront expense of > $300k, you're maybe down from $10/hr to $1.5/hr, saving something like $8.5/hr, which is $6k / month (minus the rent of whatever place you put the server in).
All in all, it's definitely feasible for a small start up as well, but not very much for an individual.