You want only child? I'll give you only child.

Coincidentally...

This is the type of determination that can be instilled in self-reliant only children: Child + Cake + 'Forbidden' = MINE NOW.
I never, to my knowledge, put my parents through anything like this for cake but I will say when you put a determined, self-reliant, calculating child who does not have siblings to rat on them in a situation where they want something desperately and you tell them, "no," that child WILL find a way. Consequences be damned, success will be ours no matter the cost because we need this (insert seemingly important item or result) and we need it NOW.
Not to degrade myself or other only children, but we pretty much turn into deviant, petulant puppies with the determination of people who have successfully climbed Everest in such situations. So if you want to know the secret of what makes some only children highly successful, it's probably because at some point during their formative years someone told them, once they had sampled the sweet deliciousness of a forbidden cake, that they could not have the cake. Those children then used all their powers of deduction, persuasion, physicality, coercion, and any other tactic they did not yet even know they name for to achieve said cake -- and most of them likely did reach the Everest peak of Cakedom and did not care that an ER visit was continually eminent for hours afterward because the only thing better tasting than ill-gotten cake is self-reliant triumph.

This from a girl who once carted her babysitter's son with her from the sitter's home to her mother's work because she wanted to see her mom. A story which will be told in full... someday.