It is never too late to teach your kid where money comes from and what it is worth. Since he is a student, his opportunities to earn will be somewhat restricted. Here is what I would do
I would tell him that I don't want to have to evaluate individual requests like "Can I have a car?" or "Can I have $100 to go out for the evening?" Instead I want to establish a budget, and give him that to spend as he sees fit. (This would be easier if his allowance in the past had been a fixed amount that he had to work out how to get what he wanted with, rather than something you can always ask for more of, but what's past is past.) He will not want to make a budget; it's hard work. So you and your wife have to agree that he gets no more money until there is a budget, and you will sit with him to do one if need be.
Make sure the budget is generous and complete. Rent, tuition, books, a transit pass, groceries, clothes, mobile phone, internet, trips home to visit you from the university city, ... make sure that you cover everything he might spend money on, even going out drinking.
Either pay his tuition and rent directly, or have a way to know they have been paid, such as knowing the password for his online banking so you can check. I wouldn't normally recommend that for grown children (I don't do it for mine), but I think in your case a little verification is important. Give him the money he needs each month, or perhaps every two weeks. Check in with him regularly: "is the budget enough? Are you able to get everything you need?" but do not comment on what he is or isn't spending. If he wants to buy clothes with this month's money and there won't be money for restaurants, or he wants to live in the clothes he has and go out drinking a lot, let him make those choices and learn how to use a limited pool of money to try to get all he needs. He should feel that you care, and want him to be looked after, but not that you are a "walking wallet" or his own personal ATM.
If he comes back and says the budget isn't enough, that he budgeted X a month for restaurants and has spent 3X already this week, here is where it gets hard. You have to tell him that the budget is fixed, he had a chance when making it with you to accurately estimate restaurant use, and now he will just have to economize elsewhere. Expect pushback. But it's much easier to discuss "raising a budget from A a month to B a month" than "giving you a car." Don't hesitate to say "we can't afford that" if it is the truth. Children often think their families are rich (not knowing about the costs of mortages, insurance, new furnaces, taxes etc), but if we can't afford something we can't afford it and that's that.
Also, try to help him observe the world more accurately, using the tradeoff information he is learning about his own budget.
- that friend who always wears the nicest clothes, whose clothes your child now wants, does that friend drive a great car? or eat in nice restaurants all the time?
- that other friend with the amazing car, how are that friend's clothes?
- and the one who eats at a different 5 star restaurant every night, what does that friend drive?
With a little perspective your son may realize that he wants everything all his friends have, but none of his friends actually have everything all his friends have. The same thing happens for adults with Facebook updates: one friend is on an amazing vacation, one is at a swim meet or something where their kid is getting medals, one just got promoted, one made a beautiful pie, one lost 50 pounds, one learned another language - but nobody did all those things and you can't measure yourself against that aggregate. (If you have the right kind of Facebook feed, show him that to make the point.)
Chances are you can't have this part of the conversation until your child has been trying to live with the budget for a while and making some of the tradeoffs. And of course it will be torpedoed if he has a millionaire friend who does in fact do all of those things. Let's hope that's not the case for your child.
Look into the recent past to see if you sometimes "cry wolf." Have you or your wife said no, even said something was impossible and couldn't be done, and then in the end done it? If so, you will have trained him to be persistent and keep going until you change your mind. You will need to address this with him directly. "I know, usually your mother will eventually give you what you want, but we are at the absolute ceiling of what we can spend on you, there is no more." And then for heaven's sake, stick to it. You aren't doing him any favours teaching him there are no limits and whining and sulking will always get you what you want.
Give him the tools he needs to be good with money. It's part of making a grownup.