Explanation:

- The surface area of a cube is calculated using the formula: $6a^2$, where $a$ is the side length of the cube.

- Given that the side length of the cube is 8 cm, the total surface area is $6\times 8^2=384{\text{cm}}^2$.

- This surface area is 128 cm${}^2$ more than the area of a square.

- Let the side of the square be $x$. Then, the area of the square is $x^2$.

- According to the problem, $384=x^2+128$.

- Solving for $x^2$, we get $x^2=384-128=256$.

- Taking the square root, $x=16\text{cm}$.

- Option 1: 16 cm

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