6. Connect any two vertices of a cube with a straight line. Among these lines, the number of pairs of skew lines that are not perpendicular to each other is:

 untranslated portion:
 在这些直线中不互相垂直的异面直线共有对.

 translated portion:
 the number of pairs of skew lines that are not perpendicular to each other is:
6. 96. There are 6 lines (4 face diagonals and 2 body diagonals) that are neither perpendicular nor coplanar with a given edge; there are 8 lines (4 edges and 4 face diagonals) that are neither perpendicular nor coplanar with a given face diagonal; and there are 6 lines (6 edges) that are neither perpendicular nor coplanar with a given body diagonal. Therefore, the number of pairs of lines that are neither perpendicular nor coplanar is $\frac{1}{2}(6 \times 12+8 \times 12+6 \times 4)=96$.