If the total surface area of a cube is 2646 cm², then find the length of each side of the cube.

It is known that the total surface area of a cube is given by 6 × (side)².

It is given that the total surface area of the cube is 2646 cm².

∴ 6 × (side)² = 2646 cm²

⇒ (Side)² = $\frac{2646}{6}$ cm²

⇒ (Side)² = 441 cm²

∴ Side = $\sqrt{441}$ cm = 21 cm

Thus, the length of each side of the cube is 21 cm.