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Ch $05$Sec$1Ex04$ MAIN $($DEPENDENT MULTI$-$PART PROBLEM $-$ ASSIGN ALL PARTS$)$

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

Let $A(n)$ be the statement that $1^3+2^3+3^3+$dots$+n^3=(\frac{n(n+1)}{2}{)}^2$ for the positive integer $n.$

Ch $05$ Sec $1$ Ex $04($c$)-$ Sum of Cubes $-$ Inductive Step

What do you need to prove in the inductive step?

$($You must provide an answer before moving to the next part$)$