Teaser 2921: Octavia the octagonarian

From The Sunday Times, 16th September 2018 [link]

Queen Octavia’s emblem was two concentric regular octagons (the outermost’s side length equal to the innermost’s distance between opposite sides). Seen from above her eightieth-birthday, level, cheesecake torte, with octagonal cavity all the way through and vertical side-faces, matched the emblem. Its outer side-faces were square and a two-figure whole number of inches wide. A four-feet diameter cylindrical cover protected it. At the party the whole torte was used, without wastage, to levelly fill a number of identical cuboid dishes (internally having length, width and depth, in inches, each a different single-figure whole number greater than one). Curiously, the number of dishes was a three-figure value with different numerals in descending order.

What was the torte’s volume in cubic inches?

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