8. The number of planes passing through the midpoints of at least 3 edges of a cube is

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As shown in the figure, there are no three points collinear among the midpoints of the 12 edges.
The cases of four points being coplanar are: (1) the 6 faces of the cube; (2) the 3 middle sections of the cube;
(3) the 12 sections parallel to the 6 diagonal planes of the cube. The cases of six points being coplanar are:

4 sections parallel to the base of the tetrahedron corresponding to the vertices.
Therefore, the number of planes passing through at least one midpoint of 3 edges of the cube is $C_{12}^{3}-$ $21 C_{4}^{3}+21-4 C_{6}^{3}+4=81$.