College Algebra problem. PLEASE SHOW ALL WORK (DO NOT skip or combine steps and

Question

College Algebra problem. PLEASE SHOW ALL WORK (DO NOT skip or combine steps and please explain what you're doing). I know the answer (it's provided with the question). I don't know how to solve the problem to arrive at that answer so I need to see ALL of the steps for arriving at the answer provided. Please TYPE your answers. I have a very hard time reading handwriting, especially if it's been scanned into the computer.

Explanation / Answer

1^3 +2^3 +3^3 .....n^3 = (n(n+1)/2)^2

Now for series : 1^3 + 2^3 +3^3 ....n^3 + (n+1)^3 +(n+2)^3

Here the last term is n+2

So, replcae n = n+2 in  (n(n+1)/2)^2

So, sum of series = ((n+2)(n +2+1)/)^2

= ( (n+2)(n+3)/2)^2

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