We are given:
Side length of the large cube = 8 cm
Side length of the smaller cube = 2 cm
We find how many smaller cubes fit along each edge:
\[
\frac{8}{2} = 4
\]
So, in each dimension (length, width, height), we can fit 4 small cubes.
The total number of small cubes in the big cube is:
\[
4 \times 4 \times 4 = 64
\]
\[
\boxed{64}
\]