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 \( r = 9 \) cm, we can substitute this value into the formula:
\[ V = \frac{4}{3} \pi (9)^3 \]
Now calculate \( 9^3 \):
\[ 9^3 = 729 \]
Now substitute this back into the volume formula:
\[ V = \frac{4}{3} \pi (729) \]
To simplify, we multiply:
\[ V = \frac{4 \times 729}{3} \pi \]
Now calculate \( \frac{4 \times 729}{3} \):
\[ 4 \times 729 = 2916 \] \[ \frac{2916}{3} = 972 \]
So, the volume of the sphere is:
\[ V = 972 \pi \]
Therefore, the volume is \( \boxed{972\pi} \) cubic centimeters.