unable to delete songs that came with ios 8 update

I recently updated my iPod to the latest update there was, which was the iOS 8 point something (I think it was 8.13), and there were some unwanted things like apps that I didn't want, but I realized that I couldn't delete them because they're "core" apps and you can't delete core apps. However, today I found out while I was listening to my music, that with the iOS update and its unwanted apps, there were also unwanted songs.

It says that I "purchased" them, when clearly I didn't, and it has a download button, but I can't delete it. Even when I download it and can delete it like that, but it doesn't disappear. It just has the download icon again. I've tried connecting to iTunes to delete it from there too, but it doesn't work either. I can delete them, but they don't disappear from my iPod.

Are these songs another "core" thing that I can't delete?