Identify 3D Tic Tac Toe type of game

Question

Looking for the name and rules of the game.

Four identical pieces. Each a clear plastic double cube with a red round bead in the center of one cube (half of the piece) and a green round bead in the center of the other cube (half). Players take turns placing each of their two pieces. Subsequent moves are made by repositioning a piece already played (following certain rules). Play is contained in a virtual 3x3x3 cube. Win with three in a row horizontal, vertical, diagonal, and/or 3D.

The game might be from 70s or 80s - not sure. Please help. I have the pieces but that's it. And pieces (pun intended) of memory.

Answer 1

This sounds like Cube Fusion, specifically the MINI Cube Fusion version as Jay A pointed out based on the number of components.

From the description:

The game includes a playing board with a 3x3 grid and 12 playing pieces. Each piece consists of two cubes, each with marbles in the center - one red, one green. Players take turns placing pieces on the board, trying to make a specified pattern in his color but not his opponent's -- all the while having to play both his color and his opponent's color each turn. There are several different games explained in the rules: make 3, 4, or 5 in a row (in 3D) before your opponent, form a square in your color, form more three-in-a-row alignments than your opponent, etc.