Explanation

3^1 = 3 > 1, 3^2 = 9 > 8, but 3^3 = 27 = 3^3, so the inequality fails at N = 3. For N ≥ 4, 3^N > N^3 by induction (3(N)^3 ≥ (N+1)^3 for N ≥ 3), so it holds for every natural N except 3.