first link below estimates that YouTube's total storage needs for all of its content are roughly 10 exabytes. It goes into a lot of detail that you can check for yourselves, because it's a bit too much to copy over here, and though I can't say it's correct for sure, the description of how they reach their calculation is quite robust.
Anyhow, if we assume storage costs for YouTube are the same as what AWS charges per month (roughly 2 cents), this would mean that it costs YT about $2.4 billion per year just to store those 10 exabytes. I'm assuming that Google can cost its storage at quite a bit cheaper than 2 cents per GB at the immense scale it operates on, so let's halve that. This still means simple storage costs of $1.2 billion per year.
These of course don't include hardware replacement, other capital costs, or the bandwidth costs of all that video being uploaded (and downloaded).
Youtube's revenues for 2019 (so a bit out of date) were nearly 16 billion (2), so while they certainly have lots of costs beyond what I described above, they're also wonderfully profitable it seems.