Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

If the function $f(x)=2x^3 - 9a x^2 + 12a^2 x + 1$, where $a>0$, attains its local maximum and local minimum at $p$ and $q$ respectively, such that $p^2 = q$, then $f(3)$ is equal to: