The volume \( V \) of a cube can be calculated using the formula:
\[ V = s^3 \]
where \( s \) is the side length of the cube. For a cube with a side length of 3 centimeters:
\[ V = 3^3 = 3 \times 3 \times 3 = 27 \text{ cubic centimeters} \]
So the correct response is 27 cubic centimeters.