As volume of the bubble

$v = \frac{4}{3} \pi (R)^3 \Rightarrow R = \left(\frac{3}{4 \pi}\right)^{1/3} (V)^{1/3} \Rightarrow (R)^2 = \left(\frac{3}{4 \pi}\right)^{2/3} (V)^{2/3}$

$\Rightarrow R^{2} \alpha V^{2/3}$

Work done in blowing a soap bubble

$W = 8 \pi R^{2} T \Rightarrow W \propto R^{2} \propto V^{2/3}$

$\therefore \frac{(\mathrm{W})_2}{(\mathrm{W})_1} = \left(\frac{(\mathrm{V})_2}{(\mathrm{V})_1}\right)^{2/3} = \left(\frac{2 \mathrm{V}}{\mathrm{V}}\right)^{2/3} = (2)^{2/3} = (4)^{1/3} \Rightarrow (\mathrm{W})_2 = \sqrt[3]{4} \mathrm{W}$