Deriving the Sum of Cubes Formula Using Difference Tables

Sum of Cubes via Difference Tables

Inspired by a Numberphile video, I explored deriving the sum of cubes formula using difference tables instead of graphical methods. By generating values and calculating successive differences, I identified the polynomial degree and solved for coefficients using Python, Mathematica, and spreadsheets. I also demonstrated a step-by-step subtraction method to isolate each term, confirming the classic result through multiple computational approaches.