backup music to the cloud

Actually there is a way to do this - for a fee.

You may subscribe to iTunes Match. Then you would be able to store your music in iCloud, regardless of where it originated.

Subscribe to iTunes Match - Apple Support

jennipharm wrote:

Can I back up music from my iPhone on to the cloud automatically? Not all of my music was bought from iTunes.

How do I back it up?

No. Those non purchase music I assume was sync to your phone via iTunes, which is were all your music should be.