1. A cube with an edge length of 3 is composed of 27 unit cubes. How many lines pass through the centers of 3 unit cubes? How many lines pass through the centers of 2 unit cubes?
There are 49 lines passing through the centers of 3 unit cubes; there are
$$
C_{27}^{2}-3 \times 49=204 \text { (lines). }
$$