$n + (n+1)^2 + (n+2)^3$ 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

Let $n=2k+1$, since it is an odd integer.
Now expand to get:
$$2k+1+(2k+2)^2+(2k+3)^3=8(k+1)(k+2)^2$$ but $(k+1)(k+2)$ is divisible by 2, since one of $k+1,k+2$ is even. Therefore the whole expression is divisible by 16.
