Putting two cubes together you get a 1x1x2 box or a dicube. Combining three dicubes 103 different pieces can be made which gives a subset of the 166 hexacubes. I sawed the dicubes cutting a 2cm x 2cm pine batten and stuck the parts together.
At last the tower with a 5x5x18 and a 3x3x18 section and the 1x1x6 piece at the top was constructed. Despite a height of 84 cm it's rather solidly built. More precisely cut pieces would allow for higher towers.
If you want to copy the construction you can sort the pieces according to the numbers and then use the attached picture of the layers.

Three 2x3x24 boxes and one 2x3x27 box can be stacked to get a 2x3x103 tower but unfortunately a construction with my pieces would surely crash.
The layers of the boxes are shown here.

You will get no problems with crashing pieces if you try the nested rings. The layers are shown here.