Problem doing induction question

[sbsbsbsb]

Homework Statement

Prove the following result using mathematical induction:
2³+4³+6³+...+(2n)³=2n²(n+1)² for all n>or=1

Homework Equations

The Attempt at a Solution

n=1:
(2(1))³=2(1)²(2)³
8=8

Assume n=k
2³+4³+6³+...+(2k)³=2k²(k+1)²

n=k+1
2³+4³+6³+...+(2k)³+(2(k+1))³=2(k+1)²(k+2)²
Using assumption
2k²(k+1)²+(2(k+1))³=2(k+1)²(k+2)²
Divide by 2(k+1)²
k²+k+1=(k+2)²
k²+k+1=k²+4k+4

I can't understand where I've gone wrong.
Any help would be greatly appreciated.

 

[sbsbsbsb]

Figured it out the second I put it up. Removed a 2³ as a 2.

 

[SammyS]

Homework Statement

Prove the following result using mathematical induction:
2³+4³+6³+...+(2n)³=2n²(n+1)² for all n>or=1

Homework Equations

The Attempt at a Solution

n=1:
(2(1))³=2(1)²(2)³
8=8

Assume n=k
2³+4³+6³+...+(2k)³=2k²(k+1)²

n=k+1
2³+4³+6³+...+(2k)³+(2(k+1))³=2(k+1)²(k+2)²
Using assumption

The following line looks as if you are assuming the very thing you are to prove.

2k²(k+1)²+(2(k+1))³=2(k+1)²(k+2)²
Divide by 2(k+1)²
k²+k+1=(k+2)²
k²+k+1=k²+4k+4

I can't understand where I've gone wrong.
Any help would be greatly appreciated.