Nope. The cake is like a fungible good -- north side of the cake is made of the same stuff as the south side, same with east-west. "But what if there's a cherry on it, and the cherry is precious?" that's only if both children want the cherry equally, and if you can equate the cherry with a volume of cake.
Voting is different because there's parts of the "cake" that is unwanted by one of the children; voters who vote against you or abstain aren't of equivalent worth to people who would vote for you. If you're proficient in gerrymandering, you can cut the cake so that both parts are toxic enough to the other kid that they can't play no matter which piece they chose to eat.
The key element here is the first-past-the-post voting system we have. You got a cake that's 67% strawberry and 33% chocolate. That's mostly strawberry, right? Cut the cake into five pieces, two are entirely strawberry (20%, 20%), the other are mostly chocolate (11%c 9%s). Now you've got 2 strawberry pieces and 3 chocolate pieces... for a chocolate majority. Doesn't matter if the strawberry-loving kid "chooses" after the "cake" is cut. This is why gerrymandering sucks. Another reason for gerrymandering sucking is the rules for making the cut. You're right that it fucking sucks the chocolate-loving kid gets to cut the next cake to make sure it mostly tastes like chocolate; the alternative, which we've already seen and may see again, is two kids wrestling over the knife and the cake growing mold while they fight (which is a weird way to say "civil war" and "military coup.")