If a sandwich is defined as any food item between two pieces of bread, then a layer cake is a type of sandwich.

The authors of salad theory actually discuss their objections to cube rule.

The cuberule theory is amusing, but tragically inconsistent. It also performs poorly against Occam’s razor (it has eight rules for categorizing food into different sections). The choice of a cube as opposed to other geometric shapes appears to be entirely arbitrary. Each category both omits common foods colloquially considered to be members of it, while including many foods that colloquially are not in it.

Cuberule food categories are extremely unstable. While amusing, we find it particularly objectionable that merely slicing or biting into a food changes its nature according to cuberule (a calzone is a calzone, but a calzone with a bite taken out of it is a bread bowl). The same applies to a burrito (calzone when fully folded, bread bowl when bitten into). Notably, a burrito with a significant quantity of carbs mixed in on the interior (e.g. burritos often contain rice) would actually be categorized as toast, which is peculiar.

By category:

1. Salad: Correctly includes a fruit salad, but would omit a caesar salad because of the croutons. It also includes things like steak.
2. Toast: correctly includes foods that are called toast. It also includes a bunch of things people don’t normally think of as to toast, like pizza and nigiri sushi.
3. Sandwich: Correctly includes most sandwiches, but not all. It excludes sub sandwiches where the bread is connected on one side (e.g., like a sandwich you’d pick up from subway). It also would include some peculiar foods, like a single layer of lasagna.
4. Taco: This correctly includes tacos, but questionably includes things like slices of pie.
5. Sushi: This category includes maki sushi, but excludes nigiri and sashimi. It also includes an unclosed burrito and a taquito.
6. Soup/Salad w/ Bread Bowl: This section includes breadbowls unless they have any rice etc in them in which case they’re toast.
7. Calzone: This section includes calzones, jelly-filled donuts, and other such baked goods, as long as you don’t cut or bite into them.
8. Cake: This section includes foods that have layers of starch, such as a hamburger.

Our position is that unintuitive inclusions are acceptable so long as there are no unintuitive exclusions. But when you have both, it’s solid evidence that your rule is wrong.