He's a bit too pleased with himself at the end there: they simply are using different algorithms, and those naturally have different performance properties for

He's a bit too pleased with himself at the end there: they simply are using different algorithms, and those naturally have different performance properties for different inputs. Feynman is relying on a prepopulated lookup table and some heuristics, while the abacus guy is relying on whichever algorithm is best suited for calculating cube roots on an abacus. Though, I admit, I'd probably be pleased as a peach too.