Mexican Math Olympiad Problem.

Number Theory Level 5

Let \(n\) be a natural number and \(1 = { d }_{ 1 } < {d}_{2} < ... < {d}_{k} = n\) its divisors, with \(k \ge 3\). Find the sum of all \(n\) such that \(n = d_2^2 + d_3^3\).