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Connect the iPod to your computer and open iTunes. In iTunes, select your iPod at top left. This will bring the Summary screen. Click on Music option on left. Enable "Sync Musics" option. Then click Apply or Sync button. This will sync all the musics from your iTunes Library to your iPod.
If you lost any purchased Musics, then you can redownload them from App Store. Follow the instructions in here --> https://support.apple.com/en-us/HT201272
If you have any questions or would like any additional information, please don't hesitate to ask.
If the Sync Musics is already checked when you access Musics in iTunes (for iPod), then uncheck it and sync the iPod again (by clicking Apply or Sync button). Then check it again and sync. Let me know if you have any difficulty and I will continue to help you.