My friend's birthday is soon and I am going to buy her a birthday cake without telling anyone and then expect to be paid back for it.
Why? Is it because you want to give the friend a surprise? Or just want to gain monetary satisfaction?
No, I do it because the guy is rich and he needs to give me money
You want money for a birthday cake you gave a friend, but that seems to be pretty shallow and greedy. He is rich but it doesn't mean he has to pay you anything. Be generous but earn your own money, you wouldn't want him to feel taken advantage of.
He can just afford it. He is arrogant and he thinks he's smarter than everyone.
Well he is your friend, isn't he? You shouldn't do things for someone and expect money back just because the person is rich-- you should do it because you want to be kind.