Question

show that a cube of any positive integer is in the form 8m, 8m+1 ,8m+3 ,8m+5 ,8m+7

Answer 1

let a be any positive integer and b=8q
Case1- a=(8q)'3
a3= (8q)3. cubing both the side
64q3, where m=q ,8m
Case2- a=(8q+1)'3
a3= use the identity (a+b)3 and apply it in (8q+1)3