Use the Principle of Mathematical Induction to Prove That $$3 \mid \left( n ^ { 3 } + 3 n ^ { 2 } + 2 n \right) \text { for all } n \geq 1$$

Use the Principle of Mathematical Induction to prove that $$3 \mid \left( n ^ { 3 } + 3 n ^ { 2 } + 2 n \right) \text { for all } n \geq 1$$