7,62,213,508 what is the next number in series

Answer 1

Try a_n = (2n)³ - n.

a₁ = 7

a₂ = 62

a₃ = 213

a₄ = 508

a₅ = ?

It helps to have memorized the first 10 or so perfect cubes to give a clue as to this sequence definition.