I am an mp3 whore. A song hoarder, and here's a tip on how to do it.
Fact1: If you have been in the web hosting business, you should know that most web servers have directory listings, and most n00b users forget to switch them off. If the web server happens to be just a file server, then its highly likely that the directory listing is on.
Fact2: The listing is cached in Google's index by the title of the page, which normally is Index of /blah blah blah.
Google for the keywords - "Index of /" + mp3 + <keywords of your song>
Eg- "Index of /" + mp3 + beatles + strawberry fields will lead you to at least one directory listing.
A word of caution though, there are advertisers and spammers out there who know this as well, so 80% of the links turn out to be dead ends, but perseverance and determination gets you there.