To find the side length \( z \) of the cube given that its volume \( V = 216 \) cubic centimeters, we start from the equation that describes the volume of the cube:
\[ z^3 = 216 \]
To solve for \( z \), we need to take the cube root of both sides of the equation:
\[ z = \sqrt[3]{216} \]
Next, we calculate \( \sqrt[3]{216} \). We can simplify this by factoring \( 216 \):
\[ 216 = 6 \times 36 = 6 \times 6 \times 6 = 6^3 \]
Thus:
\[ \sqrt[3]{216} = \sqrt[3]{6^3} = 6 \]
Therefore, the side length of the cube is:
\[ \boxed{6} \text{ centimeters} \]