Final answer:
The amount of material needed for each piece is 1014 square meters.
Step-by-step explanation:
To calculate the amount of material needed for each cube piece, we use the surface area formula SA = 6s^2, where 's' is the side length. With a given side length of 13 meters, we substitute this into the formula, resulting in SA = 6(13^2). Solving this yields a surface area of 1014 square meters. This represents the total area of all six faces of the cube. Therefore, 1014 square meters of material are needed for each cube piece to cover its surfaces.