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1.
Giving an enemy a cake anonymously for a special event. The burn lies in knowing that said enemy is enjoying the cake that you gave them, and hopefully one day will realize it was an enemy that gave them the cake - but they enjoyed it anyway. Thus creating a conflict. Only really funny to the cake giver.

Generally, a cake burn is executed within a competitive, business industry or environment.
Could be taken as a nice gesture.
Sally is having a ten year celebration for her law firm.

Competing law firm sends them a cake anonymously.

Sally is left wondering, "Who sent that delicious cake?"

Hilarious cake burn!
by Karl Bemanzoni March 07, 2014