As mentioned in your other thread, ##\lim_{x\rightarrow\pm\infty}F(x)=-\infty##. So ##F## is sometimes (you could even say way more often than not) negative. Since a sum of squares is always nonnegative, your polynomial is not a sum of squares.
Well, first off the thing that (I think) you're asking me about is a function, not an equation. Secondly, I would characterize it as a polynomial of degree six. Edit: I would also characterize this polynomial as apparently not being particularly well-suited for examination by analytic means.