The volume \( V \) of a sphere can be calculated using the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere. Given that the radius \( r \) is 9 cm, we can substitute this value into the formula:
\[ V = \frac{4}{3} \pi (9)^3 \]
First, calculate \( 9^3 \):
\[ 9^3 = 729 \]
Now substitute this value back into the volume formula:
\[ V = \frac{4}{3} \pi (729) \] \[ V = \frac{2916}{3} \pi \] \[ V = 972 \pi \]
Therefore, the volume of the sphere is
\[ \boxed{972\pi} \text{ cm}^3. \]