For a positive number $a$, let the function $f(x)$ be $$f(x) = 2x^{3} - 3ax^{2} - 12a^{2}x$$ When the local maximum value of $f(x)$ is $\frac{7}{27}$, what is the value of $f(3)$? [3 points]
For a positive number $a$, let the function $f(x)$ be
$$f(x) = 2x^{3} - 3ax^{2} - 12a^{2}x$$
When the local maximum value of $f(x)$ is $\frac{7}{27}$, what is the value of $f(3)$? [3 points]