This type of trick is old hat when it comes to hiding files on your computer itself (yes, it’ll work to hide your porn or your terrible poetry). And it can be done through any major photo sharing site.
All you have to do is rename your mp3 file to end in .jpg, upload it to the photo sharing site of your choice, and there you go. You have a file that anyone can download, and once you rename it back to mp3 it’ll play just like new.
Obviously this should only be used for files you hold the copyright to, as a quick way of downloading files from anywhere. But make sure to be careful when doing this. It may actually be against the terms of service of whatever site you choose to use, so make sure to read carefully!