I have an iPhone and I did delete it but it still shows up that I have downloaded it before and I just want it to be completely gone. How do I do that?

I've been trying to delete a song from my iTunes completely but it still shows up as if I've downloaded it before and I just completely wang it to be gone. I'be been wanting to delete this song and about 7 others and the need to delete them was made greater today. I just need these songs gone but it just won't happen. Is there any way I could fully delete these songs?