  The Mayer cluster expansion technique is applied to the Nekrasov instanton
partition function of $\mathcal{N}=2$ $SU(N_c)$ super Yang-Mills. The
subleading small $\epsilon_2$-correction to the Nekrasov-Shatashvili limiting
value of the prepotential is determined by a detailed analysis of all the
one-loop diagrams. Indeed, several types of contributions can be distinguished
according to their origin: long range interaction or potential expansion,
clusters self-energy, internal structure, one-loop cyclic diagrams, etc.. The
field theory result derived more efficiently in [1], under some minor technical
assumptions, receives here definite confirmation thanks to several remarkable
cancellations: in this way, we may infer the validity of these assumptions for
further computations in the field theoretical approach.
