There's no need to be rude. Hibbzzy got the terminology wrong, so let's help get it right.
"A song played by the piano" is a contradiction in terms. You can not play a song, you can only sing a song. So,
"a song sung by the piano" is what you should have written. Further, a piano can not sing by itself, it needs a person to do that, and this person is called a pianist. So then we get
"a song sung by the pianist". There was never a greater singing pianist than Glenn Gould, so here is an example of him singing Johann Sebastian Bach's Aria (aria=air, meaning the air a pianist has to blow out of his mouth while singing this). Try to ignore the sounds caused by him pressing down the keys of the piano and listen closely to his murmuring singing. It's not so beautifully sung, but it's a good melody.
Lastly, if the pianist keeps his mouth shut while playing it's no longer called
"a piano song", it's then called
"a piano play". For example, if Evgeny Kissin, who keeps his mouth shut while playing (and also for most part of his interviews, but that's another story), were to perform the Moonlight Sonata, you would say
"Evgeny Kissin performing the piano play Moonlight Sonata by Beethoven".Enough philosophy.