# 64 Is Not The Answer!

Algebra Level 5

$\big(x^3+y^3\big)\big(y^3+z^3\big)\big(z^3+x^3\big) \le k(x+y)(y+z)(z+x)$

Find the minimum value of $$k$$ such that $$x + y + z = 6$$ for all non-negative reals $$x,y,$$ and $$z$$.

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