1. **State the problem:** We need to find the area of a square with side length 8 cm. 2. **Formula:** The area $A$ of a square is given by the formula: $$A = s^2$$ where $s$ is the length of one side of the square. 3. **Apply the formula:** Substitute $s = 8$ cm into the formula: $$A = 8^2$$ 4. **Calculate:** $$A = 64$$ 5. **Conclusion:** The area of the square is 64 square centimeters.