To find the volume of a cube, you can use the formula:
\[ \text{Volume} = \text{side length}^3 \]
Given that the side length of the cube is 1.5 inches, we can substitute this value into the formula:
\[ \text{Volume} = (1.5)^3 \]
Calculating \( (1.5)^3 \):
1.5 multiplied by 1.5 is:
\[ 1.5 \times 1.5 = 2.25 \]
Now, multiply by 1.5 again:
\[ 2.25 \times 1.5 = 3.375 \]
Therefore, the volume of the cube is:
\[ \text{Volume} = 3.375 \text{ in}^3 \]
Rounded to the nearest thousandth, the volume is:
\[ \boxed{3.375} \]