2015's and 2016's

$P = 201520152015 \times 2016201620162016\\ =2015(100010001)(2016)(1000100010001)$

$Q = 201620162016 \times 2015201520152015\\ =2016(100010001)(2015)(1000100010001)$

The numbers are a bit long and confusing, but you should be able to see that $P=Q$

Therefore, $P-Q=0$ , and

$2016 \times (P-Q) = 2016 \times 0 = \boxed{0}$

Let's factorize $P$ and $Q$ .

$P = (2015 \times 100010001) \times (2016 \times 1000100010001)$
$Q = (2016 \times 100010001) \times (2015 \times 1000100010001)$

We see that $P$ and $Q$ are the product of the same four numbers, and therefore $P$ is equal to $Q$ . This means $P - Q = 0$ , and $2016 \times (P-Q)$ is also $0$ . $_\square$

I failed to see through the long numbers, but had a guess that turned out to be right!