i suspect the cubes part is literal and this is meant to be performed with small colored cubes. I've seen stuff just like this. I suspect the difference is the slop of piling up many cubes.

Having taught math to young kids, I used cubes at the beginning to give a real feel to the numbers. Having tangible items to play with gave them a real world demonstration of how numbers work.

And when the kids grasped the physical manipulation, I would transition to paper exercises like you are looking at. And I would call those squares "cubes." because doing so linked the physical with the abstract. And for some students, to suddenly switch terms could be confusing at first.

Teaching is about linking back to things the student already knows and is comfortable with.

We used centimeter cubes when I was a kid. Actual plastic cubes. We could use it to add length, we could use it to add volume.

For an illustration of using them for adding lengths, a 2D certainly is fine. They know what the cubes looks like, and a 3D version would just add lines they would have to ignore. Unnecessary complexity.

As an adult who knows how basic addition and basic length measurement works, I would agree with you. The cubes are simplified to squares, that's the correct name.

But for these kids that doesn't know the difference of the terms and don't need it yet, it's another simplification to avoid unnecessary complexity.

I don’t like the use of the word ‘cubes’ when ‘squares’ would have been just fine though.

I don't like either because they are actual units of measurements for volume and surface, respectively.

They're cubes, but the scaling errors are inconsistent.