A cube has 6 faces.

Total surface area of a 4×4×4 cube
= 4cm × 4 cm per face × 6 faces
= 96cm².

Now,

On each face of the 4×4×4 cube, there are only 4 unit blocks that have 1 face painted.
(The middle 4)


On each face of the 4×4×4 cube, removing these 4 unit blocks results in removing 4 exposed small square faces from the cube.


But, it also reveals another 4 small squares below these blocks, as well as another 8 on the sides that were previously blocked.


So overall, on each face, a nett total of 8 more faces are exposed.


Total surface area

= 96cm² + 8 × 1cm × 1cm for each face × 6 faces

= 96cm² + 48cm²

= 144cm²

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