Both are correct. See these examples from Macmillan dictionary.

#1 is correct You can say #2 and people will know what you mean, but I think it is technically wrong. The problem with #2 is that it is not a complete thought. "Stealing the money" doesn't convey the fact that it was HE who stole the money. "Stealing the money is not a complete thought". Who stole the money? Did anyone steal any money? If we add a few words to the end we can see that there are endless possibilities what the sentence can mean: "He admitted stealing the money was not his own idea". "He admitted stealing the money was a mistake". "He admitted stealing the money was something he was not able to do." So, you see, "stealing the money" is only part of a thought. However, if you admit TO doing something, it is like a confession. It means that you did it.

Hi Yuliya I have a student who was looking for a language partner they are B2 level, let me know if you are interested. BTW you have the same name as one of my students. 🙈

The first one