Need help! Having issues deleting music in iTunes library

I have been having issues with my iTunes library. I am currently going through my library and trying to delete older songs/artists I no longer listen to. However once I have deleted the songs I want to delete, they pop up with a cloud and a down arrow. Next it only allows me to hide the song or album. A few seconds later the song/album comes back with the same cloud and down arrow next to the song or artist or album. The same thing is happening on my iPhone? Can anyone please help me to fix this?

I would just like to permanently delete these artists/albums/songs.