What caught my eye in this question is the 2 and the -2.

Hypatia's and Euclid's numbers have a sum of 2. However, Plotemy cubes -2 twenty times. We can notice a pattern: \((-2)^3=-8,(-8)^3 = -512.\) and so on (when dealing with big numbers, look for patterns or try examples/smaller numbers). Answer this: Is there a cancellation that we can use?