To find the side length \( c \) of the cube given the volume \( c^3 = 8 \), we can solve for \( c \) by taking the cube root of both sides:
\[ c = \sqrt[3]{8} \]
Since \( 8 = 2^3 \), we can simplify this:
\[ c = \sqrt[3]{2^3} = 2 \]
Thus, the side length of the cube is \( 2 \) centimeters.