Prove the following by using the principle of mathematical induction for all `n in N`:`1^3+2^3+3^3+...+n^3=((n(n+1))/2)^2`

Explanation

To prove the statement \(1^3 + 2^3 + 3^3 + \ldots + n^3 = \left(\frac{n(n+1)}{2}\right)^2\) for all \(n \in \mathbb{N}\) using the principle of mathematical induction, we will follow these steps:

### Step 1: Base Case
We start by verifying the base case where \(n = 1\).

**Left Hand Side (LHS):**
\[
1^3 = 1
...