1. **State the problem:** We are given the radius of a spherical balloon as 21 cm and need to calculate its volume. 2. **Recall the formula for the volume of a sphere:** The volume $V$ of a sphere with radius $r$ is given by $$V=\frac{4}{3}\pi r^3$$. 3. **Substitute the given radius:** Here $r=21$ cm, so $$V=\frac{4}{3}\pi (21)^3$$. 4. **Calculate the cube of the radius:** $$21^3=21 \times 21 \times 21=9261$$. 5. **Substitute the value back:** $$V=\frac{4}{3}\pi \times 9261$$. 6. **Simplify:** $$V=\frac{4}{3} \times 9261 \times \pi = 12348 \pi$$. 7. **Approximate using $\pi \approx 3.1416$:** $$V \approx 12348 \times 3.1416 = 38796.44$$ cubic centimeters. **Final answer:** The volume of the balloon is approximately $38796.44$ cm$^3$.