iTunes radio streams use TCP 42000-42999, as per the following document:
... so blocking those ports on the network should shut down radio streams.
Alternatively, if you're in an enterprise situation with managed clients, the information on kParentalFlags_DisableRadio from the following document might be worth checking through:
If you block the following URLs, this should block iTunes Radio without blocking the rest of iTunes and the app store.
*://streamingaudio.itunes.apple.com (I'm pretty sure it's https, but I blocked both to be on the safe side.)
I've seen other documentation that mentions this site as well, but I didn't see it in the monitor.
Itunes radio block solved.
First go to settings>cellular.. turn off the music app.
This will block cellular data going to the music app.
Next go to your router's webpage and block itunes.apple.com
This will block wifi data going to the music app.
The explicit restriction doesn't work very well and the profane
words were still being heard by my children on their iphone.
I thank God he helped me figure this out