We know, Volume of sphere =$\frac{4}{3}{\mathrm{\pi r}}^3$

Given: D = 8 cm

$\therefore r = \frac{D}{2}=\frac{8}{2}=4 cm$

Therefore,

$\Rightarrow \mathrm{V} = \frac{4}{3}{\mathrm{\pi r}}^3$ $=\frac{4}{3}\mathrm{\pi }{\left(4\right)}^3$

$=\frac{4}{3}\times \frac{22}{7}\times {\left(4\right)}^3$

$= \frac{22\times 4}{21} \times 64= \frac{88\times 64}{21}= 268$

Hence, the volume is 268 cm³.