Find the value of $a^2b$ .

Find the value of $a^2b$ .

If a variable tangent to the curve $x^2y = c^3$ makes intercepts $a$ and
$b$ on the $x$ and $y$ axis respectively then find the value of $a^2b$.
The answer is $\frac{27}{4}c^3$ but how? Please show the solution steps.