How to back up music on iphone to icloud

I don't know of any way unless you subscribe to Apple Music. If not, you can always download your music purchases:

Redownload music - Apple Support

or they should be on the computer you used to sync the iPhone from originally.

You cannot.

If the music was purchased from the iTunes Store, it can be re-downloaded from there.

If it was synced from a computer, then it won't get backed up, and and should be synced from the computer again.

Apple Music only matches or uploads music from a computer, it does nothing for music already on an iOS device.

If you need to recover your music library from your iPhone, see here: link-> Recover your iTunes library from your iPo… - Apple Community