For non-zero natural numbers $x, y$, we define a new operation: $x \square y=a x^{y}+3 b x+y$. If $1 \square 2=21$, $2 \square 3=83$, then $3 \square 4=$ $\qquad$ .

Note: $x^{y}$ represents $y$ instances of $x$ multiplied together.
$607$