How did they get the term $(n+1)^3$ in the step of inductive proof which says $\sum_{k=1}^{n+1} k^3=\sum_{k=1}^n k^3 + (n+1)^3$? I'm struggling to understand on what was done in this inductive step. How did they get the $(n+1)^3$ term?  
Proof Solution


$\sum\limits_{k=1}^{\color{red}{n+1}} k^3 = 1^3 + 2^3 + 3^3 + ....... + n^3 + \color{blue}{(n+1)^3}=$
$[1^3+2^3 + 3^3  + ...... + n^3] + \color{blue}{(n+1)^3} =$
$\sum\limits_{k=1}^{\color{red}{n}} k^3 + \color{blue}{(n+1)^3}$
