How to remove songs from the iPhone without the cable?

And obviously without restoring the phone to factory settings.

Added (1). Thanks. Swipe to delete works but you can do it for whole albums too.

Nope x

Yes go into your songs section on your music app and swipe right with your finger on the song you do not want, a delete button will appear

Try to slide your finger on the song name… The delete button should pop out… You have to do it for every song… This worked on my ipad

Go to the top of your playlist. Click edit and then you can delete it from there.