Prove by induction that $1^3 + \dots + n^3 = (1 + \dots + n)^2$ I'm suppose to prove by induction:
$1^3 + \dots + n^3 = (1 + \dots + n)^2$
This is my attempt; I'm stuck on the problem of factoring dots.


Hint:
$$
(n+1)^3 =(n+1)(n+1+n(n+1))=(n+1)(n+1+2(1+2+\dots+n))\\
$$
Then 
$$
(1 + \dots + n)^2+(n+1)^3=(n+1)^2+2(n+1)(1+2+\dots+n)+(1+2+\dots+n)^2\\
=(1+2+\dots+n+(n+1))^2
$$
