This thing is a printable version of the famous Menger sponge. The 3D model is iterated up to the 4th level.
Printing the Menger sponge is a challenging task due to the many overhangs. As it has already been shown, you can succeed if you cut the sponge in half; thus, you must print the *.stl file twice and glue it together. I've cut my model in a way, that only a minimal, barely noticeable area needs to be glued together.
The model has a relatively small size: The diagonal of the square is only 9.5cm. Yet, it should be no problem to scale the model up. But keep in mind, that printing this model takes a lot of time. Printing one half in its original size took me about 15 hours with a resolution of 200 microns.
Fun Fact about the Menger sponge: If you do an infinite iteration squence, you'll end up with a body of zero volume -- but the "square's" surface will have a size of infinity!
Supports might be needed for the "large" overhang of the center of the sponge. I managed to print it without supports. Depending on your printer's bridging abilities, you might consider supports.
Infill doesn't really matter. If you print with 2 or 3 perimeter shells, then you'll almost have automatically 100% infill due to the small layer volumes.
I was able to print the sponge with a resolution of 200 microns. You should not use a higher resolution, since it could lead to the problem that the smallest squares (4th iteration) cannot be resolved anymore.