Sync 6th generation iPod nano with iCloud Music Library
Songs from Apple Music (as in your iCloud Music Library) can only be used with iOS devices, Android phones and computers running macOS or Windows.

From apple.com, emphasis mine:


  Before you can download music to listen to offline, you need to add the songs, albums, or playlists to your Library. Then, in the Music app on your iPhone, iPad, or iPod touch; in iTunes on your Mac or PC; or in the Apple Music app on your Android phone, find the song, album, or playlist that you want to download, and follow these steps: (...)