Proving the identity ∑k=1nk3=(∑k=1nk)2 without induction

I recently proved that

∑k=1nk3=(∑k=1nk)2

Using mathematical induction. I'm interested if there's an intuitive explanation, or even a combinatorial interpretation of this property. I would also like to see any other proofs.

ANSWER:-

I don't know if this is intuitive, but it is graphic.

On the outer edge of each (k+1)×k block there are k pairs of products each of which total to k2. Thus, the outer edge sums to k3, and the sum of the whole array is therefore ∑k=1nk3.
The array is the matrix product

⎡⎣⎢⎢⎢⎢⎢012⋮n⎤⎦⎥⎥⎥⎥⎥∙[123⋯n]

Therefore, the sum of the elements of the array is ∑k=0nk∑k=1nk=(∑k=1nk)2. Therefore, ∑k=1nk3=(∑k=1nk)2