6. Given a regular triangular prism with all edges of length 3, the volume of its circumscribed sphere is $\qquad$
$$
R=\sqrt{r^{2}+\left(\frac{h}{2}\right)^{2}}=\sqrt{(\sqrt{3})^{2}+\frac{9}{4}}=\frac{\sqrt{21}}{2} \text {, }
$$

So $V=\frac{4}{3} \pi R^{3}=\frac{4}{3} \pi \times \frac{21}{4} \times \frac{\sqrt{21}}{2}=\frac{7 \sqrt{21} \pi}{2}$.