We report the investigation of photonic bandgap properties of a core-shell simple cubic structure (air core with a dielectric shell) using a two-parameter level-set approach. The proposed structure can be obtained by partially backfilling high refractive index materials into a polymeric template fabricated by multi-beam interference lithography. We find that the shell formation in the inverted simple cubic structure increases the complete photonic bandgap width by 10–20% in comparison to that of a completely filled structure. The bandgap between the 5th and 6th bands begins to appear at a refractive index contrast of 2.7. This study suggests the importance to investigate the core-shell formation in three-dimensional photonic crystals through backfilling, which may offer an additional control over their photonic bandgap properties.