I have the latest iOS on my iPad and iPhone with the new Music app. I speculate the Music app's cache of downloaded streaming songs is taking about 1.5 to 2.0 GB of space, which is causing both of my devices to now report "storage almost full." This will be an issue in the future when I want to add a new app to the device. How do I clear this cache?
Some details. I activated iCloud Music Library on both devices since I'm trying out Apple Music. My iPad previously had no local audio files, but a few days after activating iCloud Music Library, the "Audio" usage on the iTunes app on OSX reported about 1.5 GB. The Music app does not show up on the iPad's General>Usage>Storage page, as there is no explicitly stored music.
My iPhone on the other hand had locally stored songs. The phone reports Music app's usage as 3.0 GB, while the iTunes app on OSX reports 4.98 GB.
EDIT: Auto music downloads are disabled on both devices
Best Answer
Easiest solution I have found so far is to disable the iCloud Music Library and open the Music app so that it can delete the cached files and/or release that storage to iOS to clear when needed.
Details: This solution is an adaptation of solutions I found for the same issue with iTunes Match. The clearing and rebuilding of your music library takes time, so I hope Apple adds a simple "clear Music cache" button to the settings in the future.
The process preserved my offline copies of songs previously synced to my iPhone prior to switching to the iCloud Music Library. I am not sure if it preserves offline Apple Music copies.