A possible connection between Mouthwashing and How Fish is Made
I've already talked about how the cake in Mouthwashing is basically a marshmallow a few times, and in any case, we know for a fact that it's made with gelatin, right? It turns out that, while gelatin can be made from any sort of bones, fish bones are a common ingredient. In other words, the fish from How Fish Is Made might have been what supplied the raw material for the birthday cake. Which also means that the one fish we see trying to eat the cake in the expansion pack was practicing cannibalism without realizing it.
The cake is the real link between the two games, essentially. That's why it appears both in the HFIM expansion with the Curly cameo and also Mouthwashing proper.