= Solution
Adding the three characteristic <quark> energies from <1/b/b> gives
$$
\boxed{m_n^{\rm estimate}c^2\sim3E_q=255.2\ \mathrm{MeV},\qquad
\frac{m_n^{\rm true}}{m_n^{\rm estimate}}\sim\frac{940}{255.2}=3.68.}
$$
The estimate recovers a sub-GeV scale but underestimates the stated <neutron> mass by a factor of a few. This is consistent with its deliberately crude uncertainty and geometry assumptions; it is not a precision mass prediction.
A better model needs the actual spatial and momentum correlations, a confining interaction, and the energy in the <quark> and <gluon> fields. In <Quantum chromodynamics>, hadron masses are not simply the sum of three freely moving particles with tiny masses. The supplied $5$ MeV rest-energy scale resembles a light current-quark scale; a phenomenological constituent-quark mass includes substantial dressing and is a different parameter. Color, spin correlations, relativistic dynamics and sea components all matter when defining a more realistic bound-state <Hamiltonian operator> or performing a <lattice QCD> calculation. The prescribed uniform-sphere model supplies none of those extra dynamical inputs, so its discrepancy should not be repaired by an unannounced change of the given radius or mass.
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