break these questions down, check if the answers are correct and explain how to get each answer.

IIL. (12 pts) Use Mathematical Induction to prove that 13+23+32++n3=n2(n+1)2 For n>1. Show all of the steps Case: N=1S(1)=1=4i2(1+1)2 +1)=13+23+33+n3+(n3+3n2+3n+1)=3(n)+(n3+3n2+3n+1)=4n2(n+1)2+(n3+n2+3n+1)=4n3(n2+2n+1)+n3+3n2+3n+1=4n4+2n3+n2+n3+3n2+3n+1=4n4+2n3+n2+44n3+12n2+12n+4=4n4+6n3+1n2+(2n+4=4(n+1)2((n+1)+1)24n4+6n2+13n2+12n+4=4(n+1)2(n+2)24n4+6n3+13n2+12n+4=4(n2+2n+1)(n2+4n+4)4n4+6n3+13n2+12n+4=4n4+6n3+13n2+12n+4