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'There are no bad foods, only bad diets'..... If you were eating cake 24/7 that would be a bad diet.  Do try to keep a sense of perspective and enjoy a slice of cake. 

I say eat a small piece of cake. It's only one day and it's not going to kill you. As long as you don't binge on it you should be fine. Celebrate the day!

You could enjoy a piece of cake and make some changes throughout the rest of the day?

Like reduce lunch by 50 cal, same for dinner and perhaps breakfast. Try to offset it somehow.

I went for dinner for a birthday two days ago and didn't feel guilty at all because I had done more exercise and ate a light lunch and snacks. And because I didn't feel guilty I thouroughly enjoyed it.