Sunday Times Teaser 2743 – Line-Up

by Nick MacKinnon

The numbers from 1 to 27 have been arranged in a 3 by 3 cubic lattice in such a way that the nine numbers on one face plane are all prime.

A table has then been created containing the sums of all triples of numbers that lie on any straight line in three dimensional space.

When the numbers on this list are summed, the result is a perfect cube.

What is this total?