In a article titled Three Dimensional Chess: Reflections and Speculations by Benjamin Grosbayne on page 74 in British Chess Magazine, Volume 85 (1964) there is one terse paragraph describing a 3D tic-tac-toe game.
"The simplest beginning for the whole 3D concept in the field of board games can be seen in QUBIC, the 3D tic-tac-toe (tick-tack-too) made by George M. Fox of Shelbourne Falls, Mass., U.S.A. This elementary game has three boards superimposed, each of five squares. The rules are as in the 2D game played by children except that the players move in three directions. The levels are held together by thin poles and the whole may be assembled or taken apart and then packed into a very small space. It should serve as a good introduction for young children and beginners in some of the following 3D games."
The only arrangement for the boards that would make sense for 5 spaces an "X" pattern.
Shelbourne Falls is evidently a misspelling since there is no such town in Massachusetts. It should be Shelburne Falls.
It is really odd that the 4x4x4 version of Qubic would later be published by "Qubic Games" in Shelburne Falls, Massachusetts.
Fox had been an employee of Milton Bradley. He evidently got the McLoughlin Brothers copies of a lot of children's books when MB bought McLoughlin. He later donated his children's book collection to the San Fransisco library.
Similar to:
3D Tic Tac Toe - Which is played on 27 spaces in a 3x3x3 grid.
Qubic - Which is played on 64 spaces in a 4x4x4 grid