I'm with those who say that money was given to the baby. Yes, the parents could spend it on their mortgage or something else, but that doesn't feel right to me. In fact, most people who gave my kids monetary gifts specifically said, "This is to jump start their education accounts".
We put aside all the money our kids received when they were born, for birthdays when they were too small to even know, etc. and saved it for their college educations. We have one in college now, and we've opted to leave that money in their accounts for the one year that they'll BOTH be in school at the same time. We figure that year'll be the toughest to pay, and we'll all appreciate the help at that point.