Friend, due to various types of issues with your phone, for example, it could be sync problem such as syncing from iTunes to Ios devices or iCloud music library issue due to a lag network connection Or maybe Apple Music server issue like termination of a song on Apple Music, pre-release or albums.

 Here are a few tricks for fixing Apple Music not playing downloaded songs:

1.       Firstly, reset Apple Music

2.      Then, by double-tapping, the home button swipe off for closing it.

3.      Next, your iPhone then reset your networking settings.

4.      After this process, launch Apple Music in another method.

5.      Now, log-out and log-in in iCloud Account.

6.      Finally, force reset your iPhone.

Another method why Apple Music is not playing:

1.       You can check out your iPhone Settings

2.      In Apple Music check that iCloud Music Library is turned on or not for seeing the music on your device.

3.      Then, disable the iCloud Music Library.

4.      Next, reset and enables it back along with this.

5.      Now, try to add a song without adding to a playlist.

6.      Again, go to settings and tap on the Apple ID profile.

7.      Later, tap on iTunes and the App Store.

8.     Finally, sign-out and back in.

 TIPS:

1.       Learn how to use Apple Music in Music App.

2.      Learn to access the song collections on your various devices.

3.      Learn how to add and download from Apple Music Catalog.

4.      Learn how to use Control Center of Ios Devices, where you can play songs also.