One of the catchiest (and educational) songs about the sun is from They Might Be Giants. But they recently had to write a new song, because scientists have learned more about what really makes the sun shine.
They Might Be Giants, Why Does the Sun Shine? (The Sun is a Mass of Incandescent Gas):
And here's the new song, with the revised theory about the sun. It's less catchy, but still informative.
TMBG, Why Does the Sun Really Shine? (The Sun is a Miasma of Incandescent Plasma):