The length of the diameter of this spherical ball is equal to the height of the box in which it is placed. The box is a cube and has an edge length of 30 cm. How many cubic centimeters of the box are not occupied by the solid sphere? Express your answer in terms of $\pi$. [asy]
draw(Circle((7.5,7.5),5));
draw((7.5,6.2)..(2.5,7.5)--(12.5,7.5)..cycle);
draw((7.5,8.8)..(2.5,7.5)--(12.5,7.5)..cycle,linetype("2 4"));
fill((2.6,7.4)--(2.6,7.6)--(12.4,7.6)--(12.4,7.4)--cycle,white);
dot((7.5,7.5));
draw((0,0)--(10,0)--(10,10)--(0,10)--cycle);
draw((0,10)--(5,15)--(15,15)--(10,10));
draw((15,15)--(15,5)--(10,0));
draw((0,0)--(5,5)--(15,5),dashed); draw((5,5)--(5,15),dashed);
[/asy]
The box has volume $30^3=27000$ cubic cm.

The sphere has radius $30/2=15$ and volume $\frac{4}{3}\pi (15^3) = 2\cdot 15 \cdot 2\cdot 15\cdot 5\pi = 30^2\cdot 5\pi = 4500\pi$ cubic cm.

Thus, the volume of the space in the box not occupied by the sphere is $\boxed{27000-4500\pi}$ cubic cm.