Of the 5 dayan cubes, guhong and zhanchi are the best 2. The guhong turns much faster than zhanchi, but zhanchi has better corner cut and can never pop unlike guhong, unless you take off the torpedos.
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The difference of their cubes is 4.
Yes, 64 = 43
When it is of the form x3 + y3 or x3 - y3. x or y can have coefficients that are perfect cubes, or even ratios of perfect cubes eg x3 + (8/27)y3.
125,216,343,512
The difference is (216 - 125) = 91 cubic centimeters.