Eiffel tower in the making

In figure 1, the number of quadrilaterals = $1$
In figure 2, the number of quadrilaterals = $3$
In figure 3, the number of quadrilaterals = $6$
(For clarification):-
In figure 4, the number of quadrilaterals = $10$
In figure 5, the number of quadrilaterals = $15$

So, we see that in the ${n}^{\text{th}}$ figure, there are $\displaystyle \sum_{i=1}^{n} i$ quadrilaterals.

So, in the ${2016}^{\text{th}}$ figure there are $\displaystyle \sum_{i=1}^{2016} i$ quadrilaterals.
= $\dfrac{2016 × 2017}{2}$ = 2033136 quadrilaterals. $_\square$