Sora's age has been discussed before, but let's summarize it. There are four important reference points:
- Start of KH1. We know Sora is 14. Let's assume his birthday was just a few days before.
- Sora creates Roxas by stabbing himself in Hollow Bastion. We have no way of knowing exactly how much time has passed between #1 and this. I'll estimate 1.5 months.
- Sora wakes up in the mansion basement in Twilight Town. This is exactly one year after #2, documented day-by-day in 358/2 Days and the beginning of KH2. It's also the last day of school summer vacation in the town.
- Sora visits Twilight Town again in KH3. HPO are on summer vacation again. Now, length of summer vacation varies by country, but about 2 months is typical. This means there must have been at least 10 months between #3 and #4.
When we add up all these time intervals, we come to conclusion that the KH3 Twilight Town visit is a couple of weeks before Sora's birthday, and because there are still several worlds to visit after this, he must have turned 16 before the end of the game. This timeline can be squeezed a little bit if the time between points #1 and #2 is shorter, and/or the summer vacation is longer, but I think the conclusion still stays the same.
Completely different question is how aging, or time in general, works in Quadratum (or more correctly, in Verum Rex world). The Foretellers seem to have been there for 1000+ years and have not aged at all...