Calculate: How Many 3cm Cubes Fit Inside a 6cm Cube?

To solve this problem, we'll follow these steps:

• Step 1: Determine how many smaller cubes (3 cm) fit along one side of the larger cube (6 cm).
• Step 2: Use the result from Step 1 to find out how many smaller cubes fit within the entire larger cube.

Now, let's work through each step:

Step 1: Calculate how many 3 cm cubes fit along one side of the 6 cm cube.
Since each side of the larger cube is 6 cm long, we divide this length by the side length of the smaller cube:

$\frac{6 \text{ cm}}{3 \text{ cm}} = 2$

This result means that 2 smaller cubes can fit along one side of the larger cube.

Step 2: Calculate the total number of smaller cubes that fit inside the larger cube.
Since cubes fit along the length, width, and height, the total number of 3 cm cubes is:

$2 \times 2 \times 2 = 8$

Therefore, the solution to the problem is $\textbf{8}$.