Calculate Cube Edge Length: Finding Sides of a 64 cm³ Cube

To find the length of the edges of the cube, we will utilize the relationship between the volume and the edge length for a cube. Specifically, the volume $V$ of a cube with edge length $a$ is given by the formula:

$V = a^3$

Given that the volume of the cube is 64 cm³, we set up the equation:

$a^3 = 64$

To solve for $a$, we need to find the cube root of 64:

$a = \sqrt[3]{64}$

Recognizing that 64 is a perfect cube, we can confirm that:

$\sqrt[3]{64} = 4$

Thus, the length of each edge of the cube is 4 cm.

This solution matches option 3, which is 4 cm, as the correct choice.