The volume \( V \) of a cube can be calculated using the formula:
\[ V = a^3 \]
where \( a \) is the length of an edge of the cube.
For a cube with an edge length of 4 cm:
\[ V = 4^3 = 4 \times 4 \times 4 = 64 \text{ cm}^3 \]
So, the volume of the cube is \( 64 , \text{cm}^3 \).