Australian AMC 2022 - Intermediate Question 22

What is the value of the following expression when $n=2022$? $$\sqrt[3]{\frac{(1\times2\times4)+(2\times4\times8)+\cdots+(n\times2n\times4n)}{(1\times3\times9)+(2\times6\times18)+\cdots+(n\times3n\times9n)}}.$$