The excess pressure \( P_{\text{excess}} \) inside a soap bubble is given by the formula:
\[ P_{\text{excess}} = \frac{4T}{r}, \] where \( T \) is the surface tension and \( r \) is the radius of the bubble.
Let the radii of the two bubbles be \( r_1 \) and \( r_2 \), and their excess pressures be \( P_1 \) and \( P_2 \), respectively.
Given:
\[ P_1 = 3P_2. \]
Using the formula for excess pressure:
\[ \frac{4T}{r_1} = 3 \times \frac{4T}{r_2}. \]
Cancelling common terms:
\[ \frac{1}{r_1} = 3 \times \frac{1}{r_2} \Rightarrow r_1 = \frac{r_2}{3}. \]
Since the volume of a sphere is \( V = \frac{4}{3} \pi r^3 \), the ratio of the volumes is:
\[ \frac{V_1}{V_2} = \left( \frac{r_1}{r_2} \right)^3 = \left( \frac{1}{3} \right)^3 = \frac{1}{27}. \]
Thus, the ratio of the volumes is \( 1 : 27 \).