Self-assembly of functionalized nano building blocks (NBBs) is a promising avenue for ‘bottom-up’ nanomaterials design. Experimental studies on functionalized polyhedral oligomeric silsesquioxane (POSS) nanocubes have revealed a wide variety of nanostructures from their assemblies. Our previous simulation studies have reproduced some of these nanostructures and predicted unusual phase behaviours imparted by the unique geometry of the nanocubes and their close packing patterns. Recent experiments further inspire us to explore the effects of tether topologies on functionalized nanocube self-assemblies. We use a simplified model and perform stochastic molecular dynamics simulations to map the morphological phase diagrams of cyclic tethered nanocubes with varying tether topology, tether number, and tether placement. Our results illustrate that the steric influence of the tethers can be manipulated to confer precise control over the self-assembled nanostructures and the phase behaviour. The novel controlling factors investigated in our study suggest new opportunities in controlling functionalized NBB self-assemblies.