Copying Podcasts Onto iPod Classic--Now That iTunes is Gone--
How do I put podcasts onto my ipod classic now that iTunes is dead?
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The Podcasts App copies downloaded podcasts to the folder /Library/Group Containers/243LU875E5.groups.com.apple.podcasts/Library/Cache. Episodes are not named or identified in any way that makes sense for us users, BUT if you can find the episode(s) you want in here, you can copy them to the desktop and/or move them onto and off of your iPod classic through a 3rd party app like iExplorer.
Without a 3rd party app that gives you access to the files on your device, you CAN copy podcasts onto your ipod classic through Apple Music, but you won't be able to delete them.