Since the area of the larger square equals the sum of the areas of the shaded and unshaded regions inside, then the area of the larger square equals $2 \times 18 \mathrm{~cm}^{2}=36 \mathrm{~cm}^{2}$.
Since the larger square has an area of $36 \mathrm{~cm}^{2}$, then its side length is $\sqrt{36 \mathrm{~cm}^{2}}=6 \mathrm{~cm}$.