This novel has noticeably inconsistencies so it hardly seems worth writing this, but I don’t think this is inconsistent. The Prince does not live alone, has a group of friends, and by this point in the book has known them a while. It seems entirely reasonable that Prince Myshkin forgot his birthday, but that Lebedev (owner of the house The Prince is living in) had learned somewhere along the way, when Myshkin’s birthday was.