  The finite size behavior of the susceptibility, Binder cumulant and some even
moments of the magnetization of a fully finite O(n) cubic system of size L are
analyzed and the corresponding scaling functions are derived within a
field-theoretic $\epsilon$-expansion scheme under periodic boundary conditions.
We suppose a van der Waals type long-range interaction falling apart with the
distance r as $r^{-(d+\sigma)}$, where $2<\sigma<4$, which does not change the
short-range critical exponents of the system. Despite that the system belongs
to the short-range universality class it is shown that above the bulk critical
temperature $T_c$ the finite-size corrections decay in a power-in-L, and not in
an exponential-in-L law, which is normally believed to be a characteristic
feature for such systems.
