Are there ties in 3D tic-tac-toe?

In a 3x3x3 tic-tac-toe game, a winning line can go through each layer of the three boards (in addition to the standard winning lines in any 2D plane of a single board). Two players play on this 3-layer board with normal tic-tac-toe rules... Problems of the Week October 16 - October 22 Basic Intermediate Advanced Solve