The volume \( V \) of a cube can be calculated using the formula:
\[ V = s^3 \]
where \( s \) is the length of a side of the cube.
Given that the side length is \( 1.5 \) inches, we can calculate the volume as follows:
\[ V = (1.5)^3 \]
Calculating \( 1.5 \times 1.5 \):
\[ 1.5 \times 1.5 = 2.25 \]
Now, multiply \( 2.25 \) by \( 1.5 \):
\[ 2.25 \times 1.5 = 3.375 \]
Thus, the volume of the cube is:
\[ V = 3.375 \text{ cubic inches.} \]
Rounding to the nearest thousandth, the final answer is:
\[ \boxed{3.375} \]