(n+1)^3 >= 3^n for n in N, n<=4

Question

Proof by Exhaustion is proving that something is true by showing that it is true for each and every case considered. Using this method (sometimes also called Proof by Cases) prove the following;

(n+1)³ >= 3ⁿ for n N, n<=4

Answer 1

There are obviously only 4 cases!

Plug in sequentially n=1, 2, 3, and 4 and show that the assertion holds for each one.