In this article, a topology inspired by nature combined with a regular honeycomb structure is proposed to enhance the flexural performance of laminated composites sandwich panels. In these cores, a bio-inspired structure based on Fibonacci spiral pattern integrated with nested hexagons was designed. The influence of the quantity of nested hexagons, in-plane orientations (W and L orientations), and possible arrangements (vertical and horizontal) of honeycomb structures on the bending performance of sandwich panels was studied through experimental and numerical approaches. The core of the sandwich structures was made of polylactic acid (PLA) polymer, while the face-sheets were made from cotton/epoxy laminated composites. The findings showed that the energy absorption of sandwich panels having three nested hexagons subjected to flexural loading in the W and L directions increased by approximately 497% and 622% compared to the conventional honeycomb baseline, respectively. Analyzing the outcomes of the present research alongside other studies revealed that while the mechanical performance of sandwich panels featuring natural composite face-sheets is typically inferior to that of sandwich structures using synthetic fiber composites or aluminum face-sheets, altering the core design can significantly enhance the mechanical properties of these sandwich panels.