I can't help doing something Can't help but do or can't help to do or can't help doing Please explain the meaning of each sentence pattern

I can't help doing something Can't help but do or can't help to do or can't help doing Please explain the meaning of each sentence pattern

Can't help but do
I cannot help you but wish you good luck.
Can't help to do
Can't help doing

I can't help crying?

I broke down and cried.
I couldn't stop myself from crying.
I couldn't help crying.
I lost it and cried.

I can't help singing
I can't help singing
How to translate
When he heard the music, he couldn't help singing
when he listens to the piece of music,
he( ）（ ）（ )a song

can't help singing
Can't help doing
when he listens to the piece of music,
he (can't）（help）（singing) a song.