But you did get a image of sorts .it seems to me that you started with some sort of visual and used that to make a logical /mathematical approach to the problem. Why would I get wrong answers ? Assuming the quality of visual varies fromperson to person those who would trust their image would just guess. If I then asked you - suppose the2 cm cube was red on the outside and white inside how many white faces would result get on 1 cm cubes. would you then resort to mathematics ? Then try this with 1 cm cubes out of a 3 cm cube . - almost impossible I think without mathematics . So i argue a strong visual image can be a disadvantage.People who trust their imagery can pick the wrong person believing they made no mistake,

This described my experience 100% When I try to answer your puzzle, I start to "visualize" the cube but it's more like a hazy, outline of a hologram that gets marginally more clear as I "focus" on certain part. I then split it into layers so I can approach it rationally. So if it's 2cm high then that means there's two layers, so I'll remember to multiply my answer I get on layer one by two. Then I split the top layer into two rows and by then it's rather obvious there's four cubes on this layer and therefore eight 1cm cubes in the 2cm cube. All that without ever having "seen" anything