Difference between square of sum (Σn)² and sum of squares (Σn²)

This is a companion discussion topic for the original entry at http://iq.opengenus.org/difference-between-square-of-sum-and-sum-of-squares/

I’m very confused by your post. The final result seems to make sense but the first line for the sum of squares: (K-1)^3 = K^3 - 3*K^2 -K + 1 doesn’t make sense.
It should be: K^3 - 3⋅K^2 + 3⋅K - 1