Answer
See below.
Work Step by Step
Proofs using mathematical induction consist of two steps:
1) The base case: here we prove that the statement holds for the first natural number.
2) The inductive step: assume the statement is true for some arbitrary natural number $n$ larger than the first natural number. Then we prove that then the statement also holds for $n + 1$.
Hence, here we have:
1) For $n=1: 1\lt2^1=2$
2) Assume for $n=k: k\lt2^k$ is divisible by $8$. Then for $n=k+1$:
$k+1\lt2^k+1\lt 2^k+2^k\lt2^{k+1}$
Thus we proved what we wanted to.