Fractal cube known as Menger's Sponge (or 3D Sierpinski's carpet).
This shape has infinite area and zero volume - it means very hard to calculate (time/memory) in higher order, and hard to 3D print-out.
I could calculate up to 4th order using PC and 3rd order using cheap FDM printer. Expecting anybody challenge more!!
I used cube.scad for OpenSCAD.
This shape is famous because of explode of calculation/memory, so 3rd order was the limit.
Another method is, generating fractal "corridor" (with cubedig.scad) copy & rotate into Z->X/Y axis direction, then subtract (boolean difference) from cube. However in this method, 4rth order was the limit. The "cubedig4-dig145.stl" is 145mm cube corridor (note: the corridor is a bit longer than 145mm). The result (resized into 1/3) is "cubedig4_48.33," generated by Blender.
After these efforts, I found my 3D printer (Da Vinci) cannot print over 3rd order - density of the object is too low, and too fragile.