  Nanowire double quantum dots occupied by an even number of electrons are
investigated in the context of energy level structure revealed by electric
dipole spin resonance measurements. We use numerically exact configuration
interaction approach up to 6 electrons for systems tuned to Pauli spin blockade
regime. We point out the differences between the spectra of systems with two
and a greater number of electrons. For two-electrons the unequal length of the
dots results in a different effective $g$-factors in the dots as observed by
the recent experiments. For an increased number of electrons the $g$-factor
difference between the dots appears already for symmetric systems and it is
greatly amplified when the dots are of unequal length. We find that in the
lowest energy states all except of two electrons form a frozen core of singlet
shells that can be separated away for description of the properties of the
system.
