Does it not look like a moustache?

In figure 1, there are $5$ quadrilaterals.
In figure 2, there are $14$ quadrilaterals.
In figure 3, there are $27$ quadrilaterals.
(For clarification):-
In figure 4, there are $44$ quadrilaterals.
In figure 5, there are $65$ quadrilaterals.

So, we see that in $n^{\text{th}}$ , there are $(\displaystyle \sum_{n=1}^{2n+1} n) -1$

So, in ${2016}^{\text{th}}$ figure, there would be $(\displaystyle \sum_{n=1}^{4031} n) -1$
= 8126496 - 1 = 8126495 quadrilaterals. $_\square$