The outer surface of a 4 cm × 4 cm × 4 cm cube is painted completely in red. It is sliced parallel to the faces to yield sixty four 1 cm × 1 cm × 1 cm small cubes. How many small cubes do not have painted faces?

The correct option is 8.

Let us analyze the dimensions of the cube and how it is sliced:
The original cube has dimensions 4 cm × 4 cm × 4 cm.
It is cut into smaller cubes of dimension 1 cm × 1 cm × 1 cm.
Along each edge of length 4 cm, there are:

$\frac{4}{1}=4$

small cubes.
Therefore, the total number of small cubes is:

$4\times 4\times 4=64$

To find the number of small cubes that have no painted faces (unpainted cubes), we look at the inner core of the original cube.
The outer layer of small cubes on all 6 faces is painted red. This means 1 unit (or 1 cube layer) is removed from all faces (front, back, left, right, top, bottom).

The dimensions of the inner unpainted cubical core are:
Length = 4 - 2 = 2 cm
Width = 4 - 2 = 2 cm
Height = 4 - 2 = 2 cm

The number of small cubes that are completely inside and have no painted faces is calculated by finding the volume of this inner core in terms of 1 cm × 1 cm × 1 cm cubes:

$\text{Number of unpainted cubes}=(4-2)\times (4-2)\times (4-2)$

$\text{Number of unpainted cubes}=2\times 2\times 2=8$

Hence, exactly 8 small cubes do not have any painted faces.