To find the number of cubes along one side of the cube, we can use the formula for the volume of a cube, which is:

$\text{Volume} = s^3$

where $s$ is the length of one side of the cube.

The total number of unit cubes used is 13824. Since the volume is equal to the number of unit cubes in the larger cube, we have:

$s^3 = 13824$

Now, we need to find $s$, the cube root of 13824. Taking the cube root of both sides:

$s = \sqrt[3]{13824} = 24$

So, the number of cubes along one side of the cube is $\boxed{24}$.

Would you like more details on how cube roots are calculated?

Here are 5 related questions:

1. What is the formula for the volume of a cuboid?
2. How do you calculate the surface area of a cube if the side length is known?
3. If the number of cubes used was 512, what would be the length of one side?
4. Can a cube with a fractional side length be formed from unit cubes?
5. What is the difference between a cube and a cuboid?

Tip: Remember that the cube of a number is that number multiplied by itself twice (e.g., $3^3 = 3 \times 3 \times 3$).