We want to determine whether obtaining an octagon as a cross section from a cube is possible. Let's first think about how an intersection of a plane and a face of a solid looks.
The intersection of a plane and a face is a line segment. The intersection of a plane and a cube can have only one line segment as an edge for each face of the cube. However, a cube has 6 faces, but an octagon has 8 sides. Since 6 < 8, it is not possible to create an octagonal cross section from a cube.
