BALTIC-WAY 2021 Problem 2

Let $a, b, c$ be the side lengths of a triangle. Prove that

$$\sqrt[3]{\left(a^{2}+b c\right)\left(b^{2}+c a\right)\left(c^{2}+a b\right)}>\frac{a^{2}+b^{2}+c^{2}}{2} .$$