To find the volume of a cube, you can use the formula:
\[ V = s^3 \]
where \( V \) is the volume and \( s \) is the length of a side of the cube. In this case, the side length \( s \) is \( 1.5 \) inches.
Now, calculate the volume:
\[ V = (1.5)^3 = 1.5 \times 1.5 \times 1.5 \]
First, calculate \( 1.5 \times 1.5 \):
\[ 1.5 \times 1.5 = 2.25 \]
Next, calculate \( 2.25 \times 1.5 \):
\[ 2.25 \times 1.5 = 3.375 \]
Thus, the volume of the cube is:
\[ V = 3.375 \text{ in}^3 \]
Rounded to the nearest thousandth, the final answer is:
\[ \boxed{3.375} \text{ in}^3 \]