My brother has been into abacuses all my life. He recently told me he’d found an obscure paper from over 100 years ago on cube roots and was working on translating it to modern abacus technique. (I hadn’t known that abacus technique changes over time, but apparently it does.) He seems to have finally done so.
Anyway, this Abacus Cube Roots page is by him and someone else in his abacus group. I won’t pretend to understand it, but from what he’s said about working it out, it sounds pretty impressive and like something he’s been trying to get right for a long time.
And I somehow figure that given the sorts of people who read my blog, some of you might just find this interesting. ;-)
(Edited to add: Shane suggested Totton’s home page as a good place to start if you’re looking for more basic information than the advanced cube root stuff, and also apparently keys to the diagrams.)