We covered each of the 64 small wooden cubes with an edge length of $2 \mathrm{~cm}$ with paper. Then we built a large cube from these small cubes. How many $\mathrm{cm}^{2}$ of paper would we save if we first assembled the large cube and then covered it with paper (we only apply one layer of paper).

(Dillingerová)
First, we will determine the paper consumption for covering 64 small wooden cubes. To cover one of these cubes, we need $6 \cdot 2 \cdot 2=24 \mathrm{~cm}^{2}$ of paper. Therefore, to cover 64 of these cubes, we will consume $64 \cdot 24=1536 \mathrm{~cm}^{2}$ of paper.

Now, we will determine the amount of paper needed to cover the large cube. This cube has dimensions of $4 \times 4 \times 4$ small cubes, which means $8 \times 8 \times 8 \mathrm{~cm}$. To cover this cube, we need $6 \cdot 8 \cdot 8=384 \mathrm{~cm}^{2}$ of paper.

The difference between these two surface areas, i.e., $1536-384 \mathrm{~cm}^{2}=1152 \mathrm{~cm}^{2}$, represents the amount of paper we would save if we first assembled the large cube and then covered it with paper.