Thank you for the suggestion, but I know that can’t be the issue because one of the examples was some songs from the “Cars” (The Movie) soundtrack, so it can’t be that it’s explicit. Also those songs were released on iTunes in 2006, and since some of the songs on the album are available I don’t get why the rest aren’t. Also these issues are on the iPad and iPhone devices I have. My father and mother also have these same issues on their iPhones.
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Edit: Also, one thing that sometimes happens if I choose To add the whole album to my iCloud Music Library and then view the album in my library, only the songs that are available on the album play, and a few minutes later other albums with the missing songs (if the song exists on multiple albums) will be automatically added to my library. (i.e. when I added the “Cars” album to my library, soon after Chuck Berry’s “Route 66” from one of his own personal albums was added to my library.