  In classical Maxwell's electromagnetism, monopole term of the electric field
is proportional to $r^{-2}$, while higher order multipole terms, sourced by
anisotropic sources, fall-off faster. However, in nonlinear electromagnetism
even a spherically symmetric field has multipole-like contributions. We prove
that the leading subdominant term of the electric field, defined by nonlinear
electromagnetic Lagrangian obeying Maxwellian weak field limit, in a static,
spherically symmetric, asymptotically flat spacetime, is of the order
$O(r^{-6})$ as $r \to \infty$. Moreover, using Lagrange inversion theorem and
Fa\`a di Bruno's formula, we derive the series expansion of the electric field
from the Taylor series of an analytic electromagnetic Lagrangian.
