What I've done is
$$\vec{L}^2 = \varepsilon_{ijk}x^jp^k\varepsilon_{imn}x^mp^n = (\delta_{jm}\delta_{kn} - \delta_{jn}\delta_{km})x^jp^kx^mp^n = x^jp^kx^jp^k - x^jp^kx^kp^j = $$
$$ = x^jx^jp^kp^k - i\hbar x^jp^j - x^jp^kx^kp^j = $$
$$ = x^jx^jp^kp^k - i\hbar x^jp^j - (x^jx^kp^kp^j - i\hbar...