Question

Hi I would like to know how I can solve this problem.

Answer 1

The $n$-th term is

$U_n = \dfrac14 n^2 (n+1)^2$

so the 39th term is

$U_{39} = \dfrac14 39^2 40^2 = \boxed{608,400}$

Observe that

$2^3 + 4^3 + 6^3 = 2^3 + 2^3\times2^3 + 2^3\times3^3 = 8\left(1^3+2^3+3^3)$

which suggests that

$V_n = 8U_n = \boxed{2n^2(n+1)^2}$