$\begin{align}  & \text{Let the G}\text{.P be }a,ar,a{{r}^{2}},--- \\ & {{S}_{\infty }}=\frac{a}{1-r}=S----(i) \\ & {{a}^{3}}+{{(ar)}^{3}}+{{(a{{r}^{2}})}^{3}}+--- \\ & {{S}_{\infty }}=\frac{{{a}^{3}}}{1-{{r}^{3}}}=\frac{64}{13}S---(ii) \\ & \text{Substitute }\frac{a}{1-r}\text{ for }S\text{ in equation (ii)} \\ & \frac{{{a}^{3}}}{1-{{r}^{3}}}=\frac{64}{13}\left( \frac{a}{1-r} \right) \\ & \frac{{{a}^{3}}}{(1-r)(1+r+{{r}^{2}})}=\frac{64}{13}\left( \frac{a}{1-r} \right) \\ & \text{Divide both sides by }\frac{1-r}{a} \\ & \frac{{{a}^{2}}}{(1+r+{{r}^{2}})}=\frac{64}{13} \\ & \text{Comparing coefficients} \\ & \text{Numerator: }{{a}^{2}}=64,\text{ }a=\pm 8 \\ & 1+r+{{r}^{2}}=13 \\ & {{r}^{2}}+r-12=0 \\ & (r+4)(r-3)=0 \\ & r=-4\text{ or }r=3 \\ & \text{The series to converge }r<1,\text{ }r=-4 \\ & {{S}_{\infty }}=\frac{\pm 8}{1-(-4)}=\pm \frac{8}{5} \\ & a,ar,a{{r}^{2}}=8,-32,128\text{ or }-8,32,,-128 \\\end{align}$