Density functional B3LYP/6-31G(d,p) calculations have been carried out to study the structural peculiarities and physical properties of the series of cubic (defect zinc-blende) silicon-carbon nitrides with composition SixC3-xN4 (x = 0, 1, 2, 3). As model systems, we have considered six clusters with the structure of the adamantane molecule (CH)(4)(CH2)(6) (I), hexamethylenetetramine-like molecules N-4(CH2)(6-n)(SiH2)(n) (II-V) (n = 0, 2, 4, 6), and silicon-substituted adamantane molecule (SiH)(4)(SiH2)(6) (VI). These 10 heavy-atom clusters have been used to simulate the crystalline fragments of diamond (I), cubic (defect zinc-blende) silicon-carbon nitrides (II-V), and cubic (zinc-blende) silicon solid (VI). It was found that the full B3LYP/6-31G(d,p) geometry optimization of these clusters allow us to reproduce the structures, unit cell parameters, and bulk modulus (hardness) of real crystals (I and VI) quite well and to predict the structural and mechanical properties of the hypothetical crystalline compounds (II-V).