Games of Great Chess normally have larger-than-normal boards, and the 8x8x8 board is bigger than any of them. Great Chess always has lots of pieces, and 8x8x8 has even more.

Games of Great Chess usually have more different kinds of pieces than there are in 8x8x8, and there are usually many fairly weak pieces to go along with a few strong pieces. I think there's a reason for this: the large number of different pieces serves to make it harder to coordinate your army, and the weak pieces make the game less tactically intense (but perhaps strategically deeper).

Games of Great Chess usually have a larger proportion of empty space on the board. This makes things a bit less tense and gives more breathing room.

Using the above ideas, it should be possible to design an 8x8x8 3D Great Chess.

P.S. according to the above ideas, Xiang Qi is a form of Great Chess.

Next, empty the outer rim of the board. Now each side has only 36 Pawns and 36 other pieces, so there's a bit more breathing room. (This also means that Castling is no longer part of the game; and with all the edge Pawns gone, the King wouldn't find as much safety there in any case.)

Now let's have a White K on 4e1, Q 4d1, RN (Chancellor) 5d1, and NB (Archbishop) 5e1.

Put White Rooks on 2b1, 2g1, 6b1, 6g1. If 1. R2b1-2a1, R2b8-1b8 is a fair reply.

Griffon 3b1 and 5g1. Black's Griffon 3b8 opposes 3b1. This piece makes a one-square diagonal move and then a Rook move away from its startingpoint, and is historically a GreatChess piece. In its 3D version, if the diagonal move rises, the Rook also rises, and so on. Example: Griffon from 3b1 to 4c3 and if empty may continue either 5c4-6c5-7c6-8c7 or 5d3-6e3-7f3-8g3

Angriff (Anti-griffon) 6c1 and 2f1. A one-square Rook move and then a bishop move; no doubt this piece already had a name, but I made up a new one because I couldn't remember the right one. Example: Angriff from 6c1 to 6d1 and then 6e2-6f3-6g4-6h5.

Throw in four Knights and Bishops, and now there are only 16 empty spaces left, enough for 4 each of 4 different pieces.

We also need them to be weak pieces, so it's pretty easy...

The (1,2,2) must of course be one of the pieces, and the others might as well be a Dabaaba, an Alfil and a Commoner.

The difficulty of remembering how so many different pieces move, let alone managing to coordinate all their different moves into an effective army, makes such a game a truly Great Chess.

There are 28 squares around the outer rim of the first rank, then 20, 12, and 4; 64 squares to fill with pieces.

There are 5 "powers": Rook, Bishop, (0,1,2), (1,1,2), and (1,2,2). There are 31 simple pieces made from combinations of one or more of these powers. What a boring lineup of pieces this would be! (And yet how logical and perfect.) On the other hand, 31 simple pieces each defined by a combination of the same 5 powers would give the player some interesting problems: how best to use them together, what are the relative values for uneven exchanges, and how to remember which is which!

In addition, of course, there are lots of other possible powers, such as the 2-space Alfil or Dabaaba jump, and it would be trivially easy to construct a game on this board with 64 different pieces in the army.

64 are too many, of course; how many should there be?

Nineteen sounds like the best compromise, four of each piece plus four unique pieces (one of which is the King).

Oh, well. This isn't really a discussion of 8x8x8 Great Chess any more, instead it has become a discussion of the theoretical problems of populating such a large board. What's worse, it isn't going to come to a conclusion.

You see, nineteen different piece types is quite a lot, perhaps too many; but on the other hand, having too many of one type also seems bad. I will leave these words here so that the next person to consider this question will have the advantage of already seeing these ideas, and go back to the main stream of 3D Chess.