Problem #WSP-5330

Problem

For non-negative real numbers $a, b, c$ prove that $a^{3} + b^{3} + c^{3} \geq \frac{(a + b + c) (a^{2} + b^{2} + c^{2})}{3} \geq a^{2} b + b^{2} c + c^{2} a .$

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