Final answer:
To find the volume of the cube, divide the sum of the lengths of all edges by 12 to find the length of one edge. Then use the formula V = s3, where s is the length of one edge, to calculate the volume.
Step-by-step explanation:
To find the volume of a cube, we need to know the length of one of its edges. Since the sum of the lengths of all the edges of the cube is given as 84 cm, we can divide this sum by 12 to find the length of one edge. 84 cm / 12 = 7 cm. The volume of a cube is given by the formula V = s3, where s is the length of one edge. Substituting s = 7 cm into the formula, we get V = 73 = 343 cm³. Therefore, the volume of the cube is 343 cm³.