<grinning> Well, he's already gotten your disappointment, & disapprobation, in addition to the punishment/humiliation in front of his friends he's already gotten at school...and will *perhaps* depending on the teacher & friends continue to get. Plus he has a punishment on the way.
I would personally reward the honesty in equal proportion to the punishment he's getting from cheating. Coldstone cones are HUGE, but *perhaps* splitting one of the kids cones with him AFTER he's been punished for cheating? Doing the whole guilt trip/standing outside the store, talking about how he would be getting an icecream cone if he hadn't cheated...and then talking about how much you value honesty, how much him being honest with you even though he knows he's losing a reward, and is going to be punished, shows how brave and kind you know he is, etc etc etc, and how no matter what he does wrong, if he's honest with you about it it will NEVER be as bad as if he hides it, or lies about it. That there is nothing wrong or bad enough TO lie or hide from you...and then take him in and split a super super small icecream as a reward for bavery in the face of adversity.
Yippee...2 whole lessons in one. Although, for me, the honesty is more important then the cheating. Cheating is never allowed. The standard though, in this culture, is for kids to lie/hide things from their parents. LOVE it when an opportunity to drive in the "tell me anything/talk to me about anything" presents itself with something concrete I can build that foundation on.
My perspective on this may be slightly different then other advice you'll be receiving. We homeschool... so the first time my son cheated on a test...I was THERE. I was the one (kind of obviously) who caught him. And because we homeschool, I found out the reasons *why* he did it, right then and there... with no filters or distractions to distort or make him forget his reasoning.
For my son it was in a couple of parts:
1) It's funny in cartoons/movies when people cheat ... and it really is. If you've ever watched them, either it's funny on purpose, or it's so overly dramatically bad that it becomes a farce, or it's so intense that the writers fairly immediately lighten the mood. So in part he was hoping for something interesting to happen.
2) Whenever *I* don't know something, I look it up. I have stacks and stacks of textbooks (college), books, and materials that I regularly go through to look up something that I've either forgotten, or to check my facts. I google questions. I go through my notes before and while teach, if I think I might be forgetting something. To my son it seemed like the smart thing to do. He was unsure, so he wanted to check and make sure he was right.
((I DO have to admit that this is fair. In school, and up to a certain level in college, our memories are tested. Once we reach a certain level in college, the tests become open book...and soooooo much harder... or are based upon your own time and research and skills at x,y,z, which is a level of hard unto itself. And in the workplace... if you don't know what something is, you'd better darn well look it up! Schools may be incredibly artificial, but they're still the standard, for many many years to come... & 90% of schooling (not education) is learning how to play the game. No it may not make sense, or be fair, or be the smartest way to do something... that doesn't mean that you get to make up your own rules in every circumstance. It also MAY make sense, be fair, and be smart. It's impossible to know without examining, questioning, and then examining the answers given... and then holding those questions and answers under the light of different circumstance. Nope. Rules don't always make sense. That DOESN'T mean that they're wrong. Whew. Try explaining all of that to a 6 year old.))
3) He wanted to see if he could.
Now.. all these parts only go together really in the mind of a 6 year old. I mean, seriously! It might be funny, & it's the smart thing to do, & see if he could??? Talk about some contradictory logic there. But that's why they're kids and in school. They're LEARNING. They're learning to think, and reason, and live, and even spell it. Their brains aren't done growing yet, and their minds are just starting to take off.
Your sons reasons are probably different (at least to a degree), but I'm willing to be that there's more then one reason... and that they're equally full of 6 year old logic. I always try to go gentle on that logic, and take each one seriously. I don't always succeed, but even in having reasons, they're showing the cognitive growth of their developing minds. Sooooo much easier to direct it NOW then when they were two. Harder lessons, certainly, then "No Hitting"...but much much much easier to redirect. :)
I don't think the pressure of a reward is "too much". I am far more inclined to reward good behavior as often as possible, then to punish for every bit of bad (not that my son thinks the same thing, I'm sure with me being me being "Mum! Dispenser of Time Outs and Punishments!!". ;) But, hey, he'll get it when he's older.
There are TONS of ways to reward good behavior and performance. If you're feeling unsure of your reward system, you might change it up a bit...with smaller rewards leading up tp a big reward over time. But that doesn't work with all kids. Some kids NEED the big reward at the end of the tunnel. Others do well with increasing levels of rewards for level of performance. What your kids respond best to, is something that you would be best qualified to know.