Basic hand tools are all that's needed.
mitre box to keep all the cuts square.
some sort of clamp.
A wood workers try-square to check all cuts.
Select a length of wood batten, oak for example, and make sure its square. My wood was 29mm square and 1 meter long, even though I only used about 820mm.
Instead of cutting 27 accurate 29mm sq cubelets, I cheated and used only 15 cuts to create 2 X 3 segment pieces, 8 X 2 segment pieces and 5 individual pieces.
Ideally all the wood grain should be jumbled up to make it harder to analyze the complete cube, but using my shortcut method this wouldn't have been possible so I'Il make fake saw cuts to simulate individual pieces.