How to stream audio on a website from cloud storage?

I know there has been some talk on here about this subject, but I'm looking for something rather specific.

I'd like a way to upload an mp3 file to a cloud storage service and then have a embed link that I can paste into my wordpress site and it'll play right on the webpage. I don't want to have a link to another site or have to download anything.

Does anyone know of such a service? The cheapest possible (it's for the website of a non-profit organization, so there's not a lot of money to go around) if such a thing exists.

If there absolutely is not this kind of service around, is there any good Plan B's?

Thanks everyone.