Lady Gaga stripped down to her thong and banged a piece of  birthday cake ... and thankfully, Terry Richardson captured the  entire thing on video tape.

Richardson -- the god-like genius who also  directed the video of Kate Upton doing the Cat Daddy in a bikini -- released  the clip on Gaga's official YouTube page.

And if you're concerned about  Gaga's personal hygiene after her romp with the dessert ... don't worry, she  takes a bath at the end of the clip.


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