29. Given a cube $12 \times 12 \times 12$, which is cut by planes parallel to its faces into unit cubes. How many parts will the cube be divided into if a section in the form of a regular hexagon is made?
65.29. Indication. Introduce a Cartesian coordinate system with the origin at one of the cube's vertices. Then the plane $x+y+z=18$ intersects the cube with a corner at point $(a, b, c)$ if and only if $15<a+b+c<18$, i.e., $a+b+c=16$ or 17 (the corner of the cube that is closest to the origin is meant). It remains to find the number of solutions to the equations $a+b+c=16,17$ in non-negative integers not exceeding 11. There are 216 in total.