Teaser 2976: Piece of cake

From The Sunday Times, 6th October 2019 [link]

Using her special recipe, so that each cubic inch of baked cake weighed one ounce, Mam made the cake for my eighth birthday party. It had a regular octagonal flat top and base, and equal square vertical faces, several inches high exactly.

Not all (but a majority) of the dozen invited pals came to the party. We each had an equal portion of cake (the largest whole number of ounces possible from it, a two-figure number). Mam had the leftover cake. Curiously, if one more or one fewer pal had turned up and our portions had been worked out in the same way, Mam’s leftover would have been the same in each case, but less than she actually got.

How large, in ounces, was my portion?

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