A3. A cube, consisting of $n^{3}$ equally sized smaller cubes, hangs in space

What is the maximum number of smaller cubes, expressed in $n$, that you can see from one viewpoint with one eye?
A3. If you look at the cube in such a way that you see three side faces, you count \( n^{2} \) cubes on the first side face, \( n \times (n-1) \) previously uncounted cubes on the second side face, and \( (n-1) \times (n-1) \) previously uncounted cubes on the third side face.

In total, therefore, \( n^{2} + (n^{2} - n) + (n^{2} - 2n + 1) = 3n^{2} - 3n + 1 \) cubes.

![](https://cdn.mathpix.com/cropped/2024_04_17_bf0efe45fea0def43891g-1.jpg?height=337&width=280&top_left_y=871&top_left_x=1505)