$n + (n+1)^2 + (n+2)^3$ is a multiple of $16$ where $n$ is odd number $n + (n+1)^2 + (n+2)^3 $
is a multiple of $16$
where $n$ is odd number
And how do i prove it.
And i tried to do with expanding but could not figured it out.
I have attached an image

HINT:
Setting $n=2m+1,$
We get  $$8m^3+40m^2+64m+32=8m^2(m-1)+48m^2+64m+32$$
Now, $\displaystyle m^2(m-1)$ is divisible by $\displaystyle m(m-1)$ which being product of two consecutive integers is even
