G1.1 Simplify $\left(\frac{1 \times 3 \times 9+2 \times 6 \times 18+\cdots+n \times 3 n \times 9 n}{1 \times 5 \times 25+2 \times 10 \times 50+\cdots+n \times 5 n \times 25 n}\right)^{\frac{1}{3}}$.
$\begin{aligned} & \left(\frac{1 \times 3 \times 9+2 \times 6 \times 18+\cdots+n \times 3 n \times 9 n}{1 \times 5 \times 25+2 \times 10 \times 50+\cdots+n \times 5 n \times 25 n}\right)^{\frac{1}{3}} \\ = & {\left[\frac{3^{3}\left(1^{3}+2^{3}+\cdots+n^{3}\right)}{5^{3}\left(1^{3}+2^{3}+\cdots+n^{3}\right)}\right]^{\frac{1}{3}} } \\ = & \frac{3}{5}\end{aligned}$