Update 06-01-19
It turns out that the 3x3x3 model wasn't quite levelled correctly, thanks to hojokono for pointing it out. I have now re-uploaded the model so that it lands squarely on the bed in your slicer.

Update 16-1--16
Added a smaller version with 15mm cubes for smaller printers.
All of the lattices are 3mm diameter.

UPDATE: Updated both models with the correct orientation for printing and added filet to bottom of bases.
Also enlarged and flared the base of the large cube for better stability and bed adhesion.

This thing was inspired by Makers Muse YT stream https://youtu.be/gfbK-orCIAY
Angus does a ton of extremely helpful videos on 3D printing.

This was my first real effort with Fusion 360, I've been dabbling with it for a week or so and was looking for ideas, then Makers Muse gave me the perfect challenge.
As you can see from the third pic, the big one came off the bed after 5 hours of printing ... should have used a skirt. Argh!
So I designed a smaller version which printed perfectly.

Print instructions

Licence: Creative Commons - Attribution - Non-Commercial - Share Alike Print Settings

Printer Brand: RepRap

Printer: Original Prusa i3 MK2

Rafts: No

Supports: No

Resolution: 0.3 and 1.6

Infill: 20% for the base, none for the rest.

Notes:

The large cube was printed @ 0.3 layer height just to check it would print ok.
The small one was printed @ 0.16 layer height
Both models had 20 infill for the base and none for the rest.