These cubes were designed by the late Dave Springett, and featured in a five page article in Issue 127 of Woodturning Magazine some years ago. Most of Dave's designs were far more complex, and featured in a book entitled 'Woodturning Wizardry'. I've attached a picture of the two tools - one a 'hook tool' for hollowing out the cubes - the other, a 'square end tool. Both just made from ground down chisels. I've attached a sketch of the processes involved, and an extract of clips from the article in Woodturning Magazine.
The article showed a wooden chuck that could be made, but I got an engineering friend to make be a set of four jaws to fit my Nova chuck, which are tubular aluminium with silicone sleeving. I've shown a pic of completed cube held in the chuck, which also shows the tool test which needs to be made on which to rest the two tools when turning, as a conventional took rest would cause the tool to snatch. A sanding platform also has to be made on which to rest the cube to ensure that all the sides are sanded perfectly square.
The last picture shows the five sacrificial plugs that need to be turned to support each finished side as the work progresses or the inner cubes could otherwise break free. The main challenge is that all the dimensions need to be exact, or for example, the holes on the inner cubes will be off centre. Hence, it's necessary to keep stopping the lathe to check with a Vernier. As the cubes are quite small, the lathe needs to be run at quite a high speed - 3,000 RPM or so. (except of course when drilling the 18mm holes with a forstner bit and and the 9mm holes).
When all the turning has been completed, the two inner cubes should just break from from the eight 'webs' on the internal corners, then the webs of the larger cube can be ground away using a Dremel and 'ball burr'.
True, they take many hours to make, and the only time I feel like making two is just before I've made one! That said, they're my favourite waste of time. For forty years until I retired my time wasn't my own, but in retirement it is, so I dance to no-one's tune but my own. I have to say that I bit my tongue when people say 'Oh I couldn't do that - I wouldn't have the patience', inferring that only attribute needed is patience.
I hope that's of interest.
There are some illustrations of the sort of work which Dave Springett was fame for on the front of his book:
Woodturning Wizardry by David Springett
This is his obituary. A much respected and sadly missed gentleman.
David Springett, Warwickshire, Rugby, England