Sums of powers via central finite differences and Newton's formula

Abstract In this manuscript we derive formula for multifold sums of powers using Newton's formula and central differences. Related works Newton's interpolation formula and sums of powers (2025) Sums of powers via central finite differences and Newton's formula (2025) Sums of powers via backward finite differences and Newton's formula (2026) Metadata DOI: https://doi.org/10.5281/zenodo.18096789 HTML: https://kolosovpetro.github.io/sums-of-powers-central-differences/ MSC2010: 05A19, 05A10, 11B73, 11B83. Keywords: Sums of powers, Newton's interpolation formula, Finite differences, Binomial coefficients, Faulhaber's formula,Bernoulli numbers, Bernoulli polynomials, Interpolation, Combinatorics, Central factorial numbers, OEIS, Stirling numbers,Eulerian numbers, Worpitzky identity.