Using binomial theorem, prove that `2^(3n)-7^n-1` is divisible by `49` , where `n in Ndot`

Explanation

To prove that \( 2^{3n} - 7^n - 1 \) is divisible by \( 49 \) for \( n \in \mathbb{N} \), we can use the Binomial Theorem. Let's go through the solution step by step.

### Step 1: Rewrite the expression
We start with the expression:
\[ 2^{3n} - 7^n - 1 \]
We can rewrite \( 2^{3n} \) as \( (2^3)^n = 8^n \). Thus, we have:
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