Ice cream cakes come in a variety of sizes, so I'm not sure why you can't buy a cake for his birthday and another for the party. Is the expense prohibitive for you? Or do you have a special bakery that provides these and so it's not possible to buy a small one? Most supermarkets have quite a selection in the freezer section. We've always bought some that serve 10 with moderate portions, which leaves a little bit of leftovers for the next day.
I think 8 year olds aren't as wrapped up in the candles and singing "Happy Birthday" though, so I'm not sure you really have to have cake & candles, unless he wants them. If he does, then do it. He hasn't had a birthday party before, so I wouldn't deprive him. However, if you are expecting friends to bring gifts, then it's best to have something to indicate it's really a birthday!
I suppose, if you are determined to have just one cake for some reason, and you are sure that the leftover cake from his actual birthday was re-frozen quickly and survived without freezer burn, you could cut it into servings and put them on plates, then present the plates to the guests. You could do this when they all sit down together and your son opens his presents. I wouldn't bring out a half cake in one piece though, because it tells the kids you are serving them leftovers.
If expense is an issue, then cut back somewhere else. 8 year olds don't care about party decor - they'll be happy with the pool party and all the fun. A lot of parents go crazy with goodie bags but I find that it's a huge expense and it's almost like people feel they have to "pay" their guests for coming.
I congratulate you on keeping the party small! We always did that, and we never succumbed to the pressure of having 25 kids at an expensive venue. Too many parents are going broke trying to put on these extravaganzas, and then everyone feels they need to reciprocate, and soon every family is spending $20 on a gift for this kid or that kid every other week. It's a huge problem. Kids don't need that - they need the fun. And a pool party in particular needs to stay manageable so that you have enough adult supervision to make sure everyone is safe, no one is diving in the shallow end, no one's holding someone under "just for fun" and all that!
I'd still give him his gifts and have a small family party on his actual day. 8 is still a little young to have to wait a month for some celebration. If you have decorations for a home party, you can certainly bring those out again at the pool party. We have reused our party decor many times over.