Identify 3D Tic Tac Toe type of game
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.