Accurate description of solvation structure of a hydrophobic nanomaterial is of immense importance to understand protein folding, molecular recognition, drug binding, and many related phenomena. Moreover, spontaneous pattern formation through self-organization of solvent molecules around a nanoscopic solute is fascinating and useful in making template-directed nanostructures of desired morphologies. Recently, it has been shown using polarizable atomistic models that the hydration shell of a buckminsterfullerene can have atomically resolved ordered structure, in which C60 atomic arrangement is imprinted. In analyzing any peculiar behavior of water, traditionally, emphasis has been placed on the long-ranged and orientation-dependent interactions in it. Here, we show through molecular dynamics simulation that the patterned solvation layer with the imprints of the hydrophobic surface atoms of the buckminsterfullerene can be obtained from a completely different mechanism arising from a spherically symmetric, short-ranged interaction having two characteristic lengthscales. The nature of the pattern can be modified by adjusting solvent density or pressure. Although solute-solvent dispersion interaction is the key to such pattern formation adjacent to the solute surface, the ordering at longer lengthscale is a consequence of mutual influence of short-range correlations among successive layers. The present study thus demonstrates that the formation of such patterned solvation shells around the buckminsterfullerene is not restricted to water, but encompasses a large class of anomalous fluids represented by two-lengthscale potential.