Abstract We compute the axion–photon coupling constant \( g_{a\gamma\gamma} \) from first principles within the \( E_8 \)–\( \mathbb{X} \) Unified Field Theory. The axion emerges naturally as a pseudo-Goldstone mode from the spontaneous symmetry breaking \( E_8 \to E_6 \times \mathrm{SU}(3)_F \), corresponding to a topological pseudo-scalar component of the fundamental field \( \mathbb{X} \in \mathbf{248} \). Using the unique representation theory of compact \( E_8 \) and the anomaly cancellation structure, we derive a parameter-free prediction \[g_{a\gamma\gamma} \approx 1.24 \times 10^{-17} \, \mathrm{GeV}^{-1},\] which lies within the sensitivity reach of current and next-generation axion experiments. This result provides a sharp, falsifiable signature of the \( E_8 \)–\( \mathbb{X} \) theory. ---