The binding of individual components to form composite structures is a ubiquitous phenomenon within the sciences. Given their ubiquity cluster nucleation and growth have been extensively studied, often assuming infinitely large numbers of building blocks and unbounded cluster sizes. These assumptions also led to the use of mass-action, mean field descriptions such as the well known Becker Doering equations. In cellular biology, however, nucleation events often take place in confined spaces, with a finite number of components, so that discrete and stochastic effects must be taken into account. We examine finite sized homogeneous nucleation and first passage time statistics by considering a fully stochastic master equation, solved via Monte-Carlo simulations and via analytical insight. We find striking differences between the mean cluster sizes obtained from our discrete, stochastic treatment and mean field results.