To find the surface area of a cube when given its volume, we start with the formula for the volume of a cube, which is:
\[ V = s^3 \]
where \( s \) is the length of a side of the cube.
Given the volume \( V = 1 \) cubic centimeter, we can solve for \( s \):
\[ s^3 = 1 \]
Taking the cube root of both sides gives:
\[ s = 1 \text{ cm} \]
Next, we can find the surface area (\( A \)) of the cube using the formula:
\[ A = 6s^2 \]
Substituting \( s = 1 \) cm into this formula:
\[ A = 6(1)^2 = 6 \text{ cm}^2 \]
Therefore, the surface area of the cube is \( 6 \) square centimeters.