Understanding nuclear behavior is fundamental in nuclear physics. This paper introduces a data-driven approach, Continued Fraction Regression (cf-r), to analyze Nuclear Binding Energy (B(A,Z)). Using a tailored loss function and analytic continued fractions, our method accurately approximates stable and experimentally confirmed unstable nuclides. We identify the best model for nuclides with A ≥ 200, achieving precise predictions with residuals smaller than 0.15 MeV. Our model's extrapolation capabilities are demonstrated as it converges with upper and lower bounds at the nuclear mass limit, reinforcing its accuracy and robustness. This data-driven approach offers valuable insights into nuclear physics and provides an illustration on the use of analytical continued fraction regression for a wide range of other possible applications.