To calculate the volume of a cube, you use the formula:
\[ V = s^3 \]
where \(s\) is the side length of the cube.
In this case, the side length \(s\) is 1.5 inches. Thus, the volume can be calculated as follows:
\[ V = (1.5)^3 \]
Calculating \(1.5^3\):
\[ 1.5 \times 1.5 = 2.25 \]
Now, multiply by 1.5 again:
\[ 2.25 \times 1.5 = 3.375 \]
Therefore, the volume of the cube is
\[ V = 3.375 \text{ cubic inches}. \]
Rounding to the nearest thousandth gives:
\[ \boxed{3.375} \]