If `P(n)` is the statement `"2^(3n)-1` . Is an integral multiple `7",` and if `P(r)` is true, prove that `P(r+1)` is true.

Explanation

To prove the statement \( P(n) \): " \( 2^{3n} - 1 \) is an integral multiple of 7" using mathematical induction, we will follow these steps:

### Step 1: Base Case
We first check the base case, \( n = 1 \).

\[ P(1) = 2^{3 \cdot 1} - 1 = 2^3 - 1 = 8 - 1 = 7 \]
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