Sunday Times Teaser 2854 – Power Surge
by Andrew Skidmore
Published June 4 2017 (link)
I recently checked my energy bills. I noticed that the account numbers for my electricity and gas are two different six-figure numbers, and that one is a multiple of the other. The electricity account number is a perfect cube and the sum of its digits is a perfect square. The gas account number is a perfect square (and, as it happens, the sum of its digits is a perfect cube!).
What is the gas account number?