What is the number of "slices" in a cube?

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Say a cube has sides of 1 cm in length
Each face of a this cube should have an area of 1 squared cm
But how many of these "areas" is the cube made of? If you were to put these 1 squared cm faces on top of each other, how many would you need to form a cube of volume equal to 1 cubic cm?

If this can't be answered because the "faces" are 2-dimensional and hence have no "depth" to speak of, how can it form a 3-dimensional figure, which has depth? If it does have some depth, what is it?