The volumes of two cubes are in the ratio 8 : 27.

Let the edges of the cubes be $a$ and $b$.

As,

$\frac{\text { Volume of the first cube }}{\text { Volume of the second cube }}=\frac{8}{27}$

$\Rightarrow \frac{a^{3}}{b^{3}}=\frac{8}{27}$

$\Rightarrow \frac{a}{b}=\sqrt[3]{\frac{8}{27}}$

$\Rightarrow \frac{a}{b}=\frac{2}{3}$

Now,

The ratio of the surface areas of the cubes $=\frac{\text { Surface area of the first cube }}{\text { Surface area of the second cube }}$

$=\frac{6 a^{2}}{6 b^{2}}$

$=\left(\frac{a}{b}\right)^{2}$

$=\left(\frac{2}{3}\right)^{2} \quad[$ Using $(\mathrm{i})]$

$=\frac{4}{9}$

$=4: 9$

So, the ratio of the surface areas of the given cubes is 4 : 9.