To find the ratio between the volumes of the first and the second soap bubble, we need to understand the relation between the excess pressure inside a soap bubble and its volume.

The excess pressure ($P$) inside a soap bubble is given by the formula:

$$P = \frac{4T}{r}$$

where $T$ is the surface tension of the soap solution, and $r$ is the radius of the soap bubble. For a soap bubble, the factor of 4 comes from having two surfaces (inner and outer), each contributing $2T/r$ to the pressure.

Given that the excess pressure inside the first soap bubble ($P_1$) is thrice the excess pressure inside the second soap bubble ($P_2$), we can write:

$$P_1 = 3P_2$$

Substituting the formula for excess pressure, we get:

$$\frac{4T}{r_1} = 3 \times \frac{4T}{r_2} \Rightarrow \frac{1}{r_1} = 3 \times \frac{1}{r_2} \Rightarrow \frac{r_2}{r_1} = 3$$

Next, we calculate the ratio between their volumes. The volume ($V$) of a sphere (or a bubble) is given by:

$$V = \frac{4}{3}\pi r^3$$

Thus, the volume ratio of the first bubble ($V_1$) to the second bubble ($V_2$) is:

$$\frac{V_1}{V_2} = \frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3} = \left(\frac{r_1}{r_2}\right)^3$$

Since we found that $\frac{r_2}{r_1} = 3$, it then follows that:

$$\frac{V_1}{V_2} = \left(\frac{1}{3}\right)^3 = \frac{1}{27}$$

Therefore, the correct option is:

Option B: $$1: 27$$