Show that cube of any positive integer is of the form 9m, 9m+1, 9m+8, for some integer m

Show that cube of any positive integer is of the form 9m, 9m+1, 9m+8,

1.	Show that cube of any positive integer is of the form 9m, 9m+1, 9m+8, for some integer m
Answer» Let a be a positive integer and b = 3. Then r =0,1or2. Case first when r is equal to zero. a= ( 3q+0)² =9q² =3(3q²)=3m where m is equal to 3q². Case second when r is equal to 1. a= (3q+1)²= (3q)²+ 23q +1²= 9q²+6q+1 =3(3q²+2q)+1 = 3m+1. Where m is equal to 3q²+2q. Case 2nd when r is equal to 2. a= (3q+2)² = (3q)²+ 23q*2 +2² =9q²+12q+4 =9q²+12q+3+1 =3(3q²+12q+1)+1 =3m+1. Where m is equal to 3q²+12q+1