Evaluate Functions and Compare Quantities

Consider the functions defined as follows:

$$ f(x) = x^3 - 6x^2 + 9x $$

and

$$ g(x) = 2x^3 - 12x^2 + 18x $$

Let $$ a $$ be the value of $$ f(3) $$, and let $$ b $$ be the value of $$ g(3) $$.

Determine the relationship between Quantity A: $$ a $$ and Quantity B: $$ b $$.