There has been a great deal of interest over the last two decades on the magnetic properties of small synthesized molecular clusters containing a finite number of magnetic ions whose positions define a three-dimensional regular structure. In many cases such molecular clusters incorporate large-spin ions whose magnetic interactions can be well described in terms of classical Heisenberg spins. In this work we calculate exactly the magnetic properties of small molecular clusters described by a classical Heisenberg model of an arbitrary number of spins all coupled equally to each other and subject to a uniform external magnetic field. We solve the problem by employing a simple mathematical approach whose idea is the introduction of auxiliary spin variables into the defining expression of the partition function. The model can be directly applied to understand the magnetic properties of recently synthesized small molecular clusters that contain a finite number of large-spin magnetic ions. © 2010 IOP Publishing Ltd.