Answer
$3$
Work Step by Step
Consider $l=\lim\limits_{(x,y) \to (1,1)} \dfrac{x^3-y^3}{xy-1}$
and $l=\lim\limits_{(x,y) \to (1,1)} \dfrac{(x-y) [x^2 y^2+xy+1]}{(xy-1)}$
Hence, $l=\lim\limits_{(x,y) \to (1,1)} x^2y^2+xy+1=(1)^2(1)^2+1 \cdot 1+1=3$
