Basic mathematics problem # 1

Algebra Level 2

If x,y,x be positive real numbers such that \[ { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }= 27, \] then what is the minimum value of \[ { x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 }? \]

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