The gradient density functional theory and Carnahan–Starling model formulated for describing the contribution of solid spheres have been used to calculate the profiles of condensate density in small critical droplets resulting from homogeneous nucleation, as well as in stable and critical droplets formed via heterogeneous nucleation on solid charged and neutral condensation cores with molecular sizes. The calculations performed for water and argon at different values of condensate chemical potential have yielded the heights of the activation barriers for homo and heterogeneous nucleation as functions of vapor supersaturation at preset system temperatures. The interaction of condensate molecules with a solid core has been described by the resultant potential of molecular attractive forces. In the case of a charged core, the long range Coulomb potential of electric forces has additionally been taken into account. Dielectric permittivities have been calculated as known functions of the local density of a fluid