Does my brother have the right to demand the money he spent on my university education, knowing that there was no agreement to repay it, and would I be sinful if I did not pay him?

If you did not possess wealth at the time your brother spent on your education, then he cannot claim it back from you. However, if you did possess wealth at the time of his spending, and he was aware of it, and he claimed that he spent with the intention of being reimbursed by you, then he is entitled to that, provided he swears that he did not spend as a volunteer. What appears from the question is that you did not possess wealth at the time your brother spent, and therefore he has no right to claim anything back from you. You, however, should maintain ties with him and appreciate his kindness.