Detrimental

Let $A(x)=$
$$\begin{array}{}& \left|\begin{array}{ccc}x& 2x& x^2\\ x+1& 2x+1& x^2+1\\ x+2& 2x+2& x^2+2& \end{array}\right|\end{array}$$ including the determinant operator.

Compute the sum of all $A(x)$ where $x$ varies from $1$ to ${10}^9$ inclusive.