You would need to contact Mojang about this, since this forum is not owned or operated by Mojang or Microsoft. Here may be a starting point as to what their usage guidelines are and how to contact them:
I'm not sure about the newer music, but I think the old stuff was originally chosen for the game because it was free to use. I may be wrong about that, but you might want to look into it. If I'm right you can use the classic stuff without worrying about permission
If you want to play Minecraft with the music, no-one will ever bother.[/b]
But if you want to play the music separately from Minecraft, the music producers has its own term and different qualification.[/b]
Youtube will bother, and because it can be a hassle to pull your video back out from a DRM complaint most if not all youtubers will simply turn off the music or turn it way, way down so the viewer can't actually hear it clearly. Fallout 4 had radios all over the place that were turned on, it made sense to have them in the game but because they played songs that weren't necessarily free-to-use as a youtuber you had to go around turning them all off. Another game (umm, Mafia?) was set in 1970s and you drove around in cars with working radios--that played exactly the songs you would find on the radio in real life (listening to them in your car, that's fine; listening to them in a game video you're offering up to the public...not so fine).