Recording a cover song isn't really super expensive... in general all you need a mechanical license (which you have to obtain from the label/publishing company, which is usually the trickiest part). From there all you have to do is pay $0.09 per copy (if the song is less than 5 minutes long). The pricing is a little different if the song is longer than five minutes (I don't remember exactly but I think it's like $0.018 per minute, rounded up to the nearest minute). So it's really not that expensive compared to some other licenses.