2. If positive integers $a$, $b$, and $c$ satisfy $a b + b c = 518$, $a b - a c = 360$, then the maximum value of $a b c$ is $\qquad$ .
2. 1008 .

From $ab+bc=518, ab-ac=360$, subtracting the two equations, we get $c(a+b)=2 \times 79$.
Upon verification, taking $c=2, a+b=79$, then $ab=518-bc=518-2b$.
Upon inspection, when $b=7$, $ab$ reaches its maximum value of 504. Therefore, the maximum value of $abc$ is 1008.