Please make sure the music is playable before you transfer:
#1 Play the converted music through the media player to check if it is successfully converted, like Windows Media Player or iTunes.
#2 If it is still unplayable, please use some online music converters to convert the music again in order to get the non-DRM MP3 music files.
If you have checked that the music is playable and DRM-free, please follow the steps below.
#1 Delete the original downloaded music from iTunes.
#2 Turn on iTunes and click "Files" > "Add Files to the Library".
#3 Choose the converted music and add to iTunes.
#4 Create a playlist and move all the converted music to this playlist. Or just go to the playlists named as Recently Added or New Added, this is the music you just add to the music library.
#5 Plug in the USB cable to iPod and connect to the iTunes.
#6 On the main interface of iPod, choose music > Sync and then select the Recently Added/New Added/Created playlist and sync to your iPod.
#7 Please make sure to Remove and Sync the content to your iPod and then you can successfully add the music to iPod.
Related Articles: Can't Sync Apple Music to iPod shuffle? Solved!