How can I make 3d grid based movement for a strategy game on the y axis

Hello, I'll try my best to be as descriptive as possible. I'm currently at the beginning of development for a game I intend to be similar in gameplay to Fire Emblem, with some twists. The most important one and the one I'm asking about here is I'm looking for the best way to implement a fully 3d grid on all axis. An example would be If I have a cube with flat ground and no elevated terrain if I have a unit that can fly they can move anywhere in that cube even though there's no ground under them. I've also included a really crude drawing that I put together for this example that can hopefully illustrate what I'm trying to ask. Even if someone can just point me in the general direction that'd help so much. With all the research I've done I can't seem to find a tutorial or even a game that uses this system so I'm at a loss as to where to start.