Show that $1^3+2^3+....+n^3=(1+2+3+...+n)^2$

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I use induction N=1 And n=k But in case of n=k+1 i can't write the thing .help

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Answer 1

Hint: Expand the right side as $((1+2+3+\ldots+n)+(n+1))^2$ The square of the first term is the sum of the cubes up to $n$ by the induction hypothesis. The cross term is $2(n+1)\frac 12n(n+1)$