If $a : b = 2 : 3$, then find the value of $(7a^3 – 2b^3) : (b^3 – a^3)$.

Given:

a : b = 2 : 3

Let,

$a = 2x,; b = 3x$

Now substitute in the expression:

$\frac{7a^3 - 2b^3}{b^3 - a^3}$

$a^3 = (2x)^3 = 8x^3$

$b^3 = (3x)^3 = 27x^3$

Substitute:

$\frac{7(8x^3)-2(27x^3)}{27x^3-8x^3}$

$= \frac{56x^3-54x^3}{19x^3}$

$= \frac{2x^3}{19x^3}$

$= \frac{2}{19}$

Final Answer: 2:19