3. The number of trapezoids formed by the $4 n+2$ vertices of a regular $4 n+2$-sided polygon is $\qquad$ .
$$
5.2 n(2 n-1)(2 n+1) .
$$

A regular $4 n+2$-sided polygon has $2 n+1$ diameters. All trapezoids can be divided into two categories: one with bases parallel to a certain diameter, and there are $(2 n+1)\left(\mathrm{C}_{2 n+1}^{2}-n\right)$ such trapezoids; the other with bases perpendicular to a certain diameter, and there are $(2 n+1)\left(C_{2 n}^{2}-n\right)$ such trapezoids. Therefore, the total number of trapezoids is $2 n(2 n-1)(2 n+1)$.