MI - To prove divisibility (solution)

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2^3 -2=6=(2^2 - 1)2
3^3-1=24=(3^2-1)3

k^3 -k =(k^2-1 )k
means k is divisible by 3 0r K^2-1 is divisible by 3
so (k+1)^ - (k+1) = ((k+1)^2 -1)(k+1) = k(k+1)(k+2)
k is divisible by 3, so it is valid for k+1 th term
is this prove is true??

amarprakash