To solve this problem, we must first understand the configuration and dimensions of the solid shapes involved.

We are given that we have three identical solid cubes, each with a side length of 2 cm. The cubes are placed one over another to form a cuboid.

The volume of a cube is given by the formula:

V_{\text{cube}} = a^3, where a is the side length of the cube.

Substituting the given side length of the cube, we have:

V_{\text{cube}} = (2 \, \text{cm})^3 = 8 \, \text{cm}^3

Since three cubes are stacked to form the cuboid, the dimensions of the resulting cuboid become:

• Length = 2 cm (same as the side of a cube)
• Breadth = 2 cm (same as the side of a cube)
• Height = 3 × 2 cm = 6 cm (because three cubes are stacked vertically)

Now, the volume of the cuboid is calculated using the formula:

V_{\text{cuboid}} = \text{Length} \times \text{Breadth} \times \text{Height}

Substituting the measurements:

V_{\text{cuboid}} = 2 \, \text{cm} \times 2 \, \text{cm} \times 6 \, \text{cm} = 24 \, \text{cm}^3

Therefore, the volume of the resulting cuboid is 24 \, \text{cm}^3.

Upon analysis of the options given:

• 8 \, \text{cm}^3: This is the volume of a single cube, not the cuboid.
• 16 \, \text{cm}^3: This is not correct as it doesn't account for stacking three cubes.
• 24 \, \text{cm}^3: This matches our calculated volume of the cuboid.
• 32 \, \text{cm}^3: This is incorrect based on our calculations.

Thus, the correct answer is 24 \, \text{cm}^3.