The volume of a sphere is given by the formula $\frac{4}{3}\pi r^3$.
The volume of the larger sphere is $\frac{4}{3}\pi(6^3) = 288\pi$ cubic units.
The volume of the smaller sphere is $\frac{4}{3}\pi(3^3) = 36\pi$ cubic units.
The volume of the region within the larger sphere and not within the smaller sphere is the difference between the two volumes, which is $(288\pi) - (36\pi) = \boxed{252\pi}$ cubic units.
The answer is: 252\pi
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
There are two concentric spheres of radii 3 units and 6 units. What is the volume, in cubic units, of the region within the larger sphere and not within the smaller sphere? Express your answer in terms of $\pi$.

### Answer:
