Q: Can I download my Apple Music library onto my 64 gig Apple TV so it will still work when the wifi isn't working?

No. Apple TV 4 can stream your purchased content from the iTunes Store, more if you have an active iTunes Match or Apple Music subscription, play media from a locally accessible shared library, or you can Air Play content from a device or computer. The onboard storage can be used for apps. but there is no locally stored media cache for use offline.

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