$\begin{aligned} & \frac{a_1+a_2+a_3+\ldots \ldots+a_p}{a_1+a_2+a_3+\ldots \ldots+a_q}=\frac{p^3}{q^3} \\ \Rightarrow & \frac{a_1+a_2}{a_1}=\frac{8}{1} \Rightarrow a_1+\left(a_1+d\right)=8 a_1 \\ \Rightarrow \quad & d=6 a_1 \\ & \text { Now } \frac{a_6}{a_{21}}=\frac{a_1+5 d}{a_1+20 d} \\ = & \frac{a_1+5 \times 6 a_1}{a_1+20 \times 6 a_1}=\frac{1+30}{1+120}=\frac{31}{121}\end{aligned}$