Cover versions of songs in free podcasts?

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Some friends and I have released a pilot for a new podcast ("The 3rd Edge") on iTunes, and will be commencing new episodes soon. We have had an idea to finish off each episode with a different cover version of a song, obviously with the music and vocals recorded by ourselves. What we'd like to know is are we actually allowed to? I've seen cover versions of songs on youtube and similar sites and they are still there, and even uploads of the actual original recording by the original artist, so that would suggest you can re-record other peoples music if you are making no profit, but is it actually legal? What would we need to do in order to be able to do it if we are unable to do it regardless? Thank you