Numerical Methods: Euler to Runge–Kutta · Superchallenge problem

Heun's method is applied to the harmonic oscillator $x' = y$, $y' = -x$ from $(x_0, y_0) = (1, 0)$, using $n$ steps of size $h = \dfrac{2\pi}{n}$ to cover one full period. Let $\rho_n = x_n^2 + y_n^2$ after those $n$ steps. Find $\displaystyle\lim_{n \to \infty} n^3(\rho_n - 1)$.