Knowing the interactions controlling aggregation processes in magnetic nanoparticles is of strong interest in preventing or promoting nanoparticles' aggregation at wish for different applications. Dipolar magnetic interactions, proportional to the particle volume, are identified as the key driving force behind the formation of macroscopic aggregates for particle sizes above about 20 nm. However, aggregates' shape and size are also strongly influenced by topological ordering. 1-D macroscopic chains of several micrometer lengths are obtained with cube-shaped magnetic nanoparticles prepared by the gas-aggregation technique. Using an analytical model and molecular dynamics simulations, the energy landscape of interacting cube-shaped magnetic nanoparticles is analysed revealing unintuitive dependence of the force acting on particles with the displacement and explaining pathways leading to their assembly into long linear chains. The mechanical behaviour and magnetic structure of the chains are studied by a combination of atomic and magnetic force measurements, and computer simulation. The results demonstrate that [111] magnetic anisotropy of the cube-shaped nanoparticles strongly influences chain assembly features.