Prove with the definition of function limit: limx ^ 3 (x tends to 2) = 8

Prove with the definition of function limit: limx ^ 3 (x tends to 2) = 8

For any positive number ε > 0, take δ = min (ε / 20, 1),
If | X-2 | < δ, 1 < x < 3,
So | x ^ 3-8 | = | X-2 | * | x ^ 2 + 2x + 4 | < ε / 20 * (9 + 6 + 4) < ε,
So LIM (x → 2) x ^ 3 = 8