Here are two cubes, A and B - Edexcel - GCSE Maths - Question 8 - 2022 - Paper 1

For cube B, the side length is 4 cm:

$V_B = 4^3 = 64 \text{ cm}^3$

Density is given by the formula: ( \text{Density} = \frac{\text{mass}}{\text{volume}} ).

For cube A:

density of cube A = ( \frac{81 \text{ g}}{27 \text{ cm}^3} = 3 \text{ g cm}^{-3} )

For cube B:

density of cube B = ( \frac{128 \text{ g}}{64 \text{ cm}^3} = 2 \text{ g cm}^{-3} )

The ratio of the densities of cube A to cube B is:

$\frac{\text{Density of A}}{\text{Density of B}} = \frac{3}{2}$

Thus, the answer in the form a : b is: ( 3 : 2 ).