If your current sub panel is fed with something like 10-3 copper, your sunk.Alrightie then...there's the answer....looks like my goose is cooked. .If he installed #10 because that's all he'd need for a 30A sub panel, then the answer is no
The feed line is 10-3 - so- - I'm stuck with what I've got.
"Life is what happens to you while you're busy making other plans." - John Lennon
The other answers say this but I will say it differently. The breaker must match the wire size. It can be smaller than the safe load on the wire but it cannot be bigger. If you put a big breaker on a small wire you risk overheating and a fire.
It boils down to, what size wire was used to feed this panel. The breaker is there to protect the wire so it NEEDS to be sized properly to insure the load isn't too much. If the load is too much it can over heat the wire and be a serious fire threat.