You can get some free AWS servers but the amount of storage and traffic you get is very low.
I'm not sure what the cost is once you go past the free tier but yeah its probably way higher than the amount you would mine,
and since its CPU mining it would have to be Etherium or some altcoin, right?
Storage and bandwidth (I think you mean bandwidth when you say traffic) aren't really important factors for mining. Modern mining programs are lightweight and can use very little bandwidth (especially if you set a very high share difficulty, but that probably isn't a good idea). Like -ck mentioned, it wouldn't make sense to mine straight bitcoin on a cloud instance. However, if you're able to get an instance for a third of the price and you're able to jump on a new CPU-only coin, there's a chance you'd be able to make some money. I remember some people used cloud instances a couple years ago to mine CPU-only coins as soon as they released, and some of them were able to make a bit of money. Keep in mind that they only used these cloud servers to mine for short periods of time (days or a couple weeks usually) because usually it costs more to pay for the server than you'd be able to earn from mining. Additionally, some VPS providers will shut servers down when they see that they're being used for mining, because of the huge drain on CPU resources that mining uses. I'm not sure what Amazon's policy on mining is, but that's something you should keep in mind.