Prove the inequality $(x+y+z)^3>27(y+z-x)(z+x-y)(x+y-z)$

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I was trying to prove the equation

$(x+y+z)^3\gt27(y+z-x)(z+x-y)(x+y-z)$

I've proved $(x+y+z)\gt 27xyz$ before by AM-GM inequality. However, I'm confused with what I should do to prove this equation. Can you help?