What is the Big-Ω of the following function?
$$\begin{align}
\sum_{x=1}^{2n}(x+x^2) \gt \sum_{x=1}^{2n}x^2 \gt \sum_{x=n+1}^{2n}x^2\gt\sum_{x=n+1}^{2n}n^2= n^3
\end{align}
$$

So the function is $\Omega(n^3)$. You have shown it is $O(n^3)$. So the function is $\Theta(n^3)$.

Although $n^3$, the asymptotic lower bound ignoring a constant factor is the same as the asymptotic upper bound ignoring a constant factor in the current case, it is not always true because some functions fluctuate. For example,
$$f(n)=\begin{cases}1 \quad \text {when }n\text{ is odd,}\\ n \quad \text{when }n\text{ is even.}\end{cases}$$ $f(n)=O(n)$ and $f(n)=\Omega(1)$. Both bounds are tightest.



Exercise. Show that $$\sum_{x=1}^{m}(x+x^2)=\frac{m(m+1)(m+2)}{3}$$