Calculate Cube Volume: Finding Volume from 4 cm² Base Area

To solve this problem, we'll determine if we can calculate the volume of the cube and, if possible, proceed with the calculation.

First, we need to find the side length of the cube. The given area of the base is $4 \, \text{cm}^2$, indicating that each face of the cube is a square. Thus, we have:

$s^2 = 4$

To find $s$, the side length $s$, we take the square root of both sides:

$s = \sqrt{4} = 2 \, \text{cm}$

Now that we know the side length, we can calculate the volume of the cube using the formula:

$V = s^3 = 2^3 = 8 \, \text{cm}^3$

Therefore, it is indeed possible to calculate the volume of the cube. The volume is $8 \, \text{cm}^3$.

The correct choice, reflecting this calculation, is $\boxed{8}$.