I see the problem. You are comparing the 4680 cell with the 21700 cell. I am comparing the 4680 cell with the 18650 cell. Now which cells was Tesla comparing?
The 4680 cell is 132952 mm3 in volume.
The 21700 cell is 24245 mm3 in volume.
The 18650 cell is 13069 mm3 in volume.
The cells are cylindrical in shape, not cubed.
PS. I used this website for volume calculations https://www.calculator.net/volume-calculator.html?
But you got it wrong. In your first message you use 8 as the radius of an 18650. Half of 18 is 9, not 8.
9 x 9 x 65 x PI = ~16540 mm3
I think the other two calculations are correct.
The primary purpose of the larger cells is to drive down manufacturing costs. Fewer cells means fewer parts, fewer manufacturing and assembly operations, and fewer potential failure points.
The new form factor also may make the use of the cells as structural components more tenable. The aspect ratio between cell diameter and height is more favorable from a structural perspective. Is the wall thickness the same? I don’t know.
Despite all the online speculation otherwise, when Tesla introduced the 2170 format Elon said the primary driver was cost. It’s likely the same for the 4680.
The tabless design makes the larger cell practical, solving cooling and charge/discharge rate issues with a traditional single tab in such a large cell. It might also benefit the smaller form factors.
Regardless of the cells, it’s the pack as a whole that matters. Certainly eliminating the cooling ribbon used by the 18650 and 2170 packs will improve the horizontal density of the Tesla battery pack.