Minimum value#3

Algebra Level 4

Non-negative real numbers $a,b,c$ are such that $a+b+c=2017$ . Find the minimum value of

$C=\sqrt [ 3 ]{ 4\left( { a }^{ 3 }+{ b }^{ 3 } \right) } +\sqrt [ 3 ]{ 4\left( { b }^{ 3 }+{ c }^{ 3 } \right) } +\sqrt [ 3 ]{ 4\left( { c }^{ 3 }+{ a }^{ 3 } \right) } .$