Proving sum of cubes formula with counterexample and induction

[hannahlawe]

hi this question i just cannot do. i have no idea where to start:

a student is trying to recall the formula for the sum of cubes of consecutive numbers. she thinks it may be (n^3(n+1)^3) /8 or (n^2(n+1)^2)/4 . show by counter example one is incorrect and the other is correct by induction.

i can do the induction part its just the counter example i don't know where to start! thanks you

 

[mathman]

Try different n's, at some point (n=2) they give different results.