Sunday Times Teaser 2921 – Octavia the Octagonarian

by Stephen Hogg

Published September 16 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?