You can use the fact that the right side is just a square of a ordinary arithmetic sum.
sum = n/2(a_1+a_n)
i did use the base case and find it true
1=1
0^3+1^3=0+1*0+1
im not good with latex but in my paper the right side just to make it more "simple" for me i did write it as 2 times that instend to have ^2...
ima proof for k+1 and need tips :S im lost