There is no easy way out of this situation at all. In fact, there isn't really a way out at all.
If you've been caught cheating, whether it is with another person, or cheating someone out of money, you're in the dog box and there you will stay for quite a while. In fact, don't be surprised if you've been cheating on your partner and you get dumped.
There are some things for which "I'm sorry", just is not enough. The best you can do is to look sorry, to say so and be prepared to hit the road. Remember the other person has every right in the world to be hurt and incredibly angry – you presented yourself as trustworthy, he/she believed you and now they've come short as a result of it.
When it comes to money and relationships, honesty is always the best policy, even if it means unpleasantness.
Read the following article on whether trust can be rebuilt after an affair.