In additive manufacturing, while maintaining a constant mass flow rate, operations involving temperature-induced expandable materials show an increase in the volumetric flow rate during their expansion at the nozzle exit. This research uses foamable filaments made of thermoplastic elastomers (TPEs) and thermally expanded microspheres (TEMs) to examine this increase in volumetric flow rate relative to the theoretical mass flow rate at the nozzle exit during fused filament fabrication (FFF). Adjusting the volumetric flow rate and material attributes enables continuous 3D printing of hybrid thermoplastic elastomer foam samples with a density gradient. This is achieved by real-time adjustments to printing temperature and layer height. Using TEMs with a greater starting expansion temperature (relative to the filament melting temperature) allows for a linear density decline from 200 to 240°C, allowing for the fabrication of a gradient density structure by manipulating 3D printing parameters. The pressure-volume-temperature investigation indicates that the expansion ratio of the foamable filament increases with TEM weight percent (wt.%) and a reduction in pressure, but the mass remains the same. Using the FFF technique volume conservation principle, custom G-codes are developed for strand analysis and hybrid cube production. It is observed that the layer height has a linear connection with flow rate, which increases with temperature up to 2.5 times the predicted mass flow rate at 240°C for 10 mm/s printing. The material flow rate is key to controlling the foamable filament expansion, through which parts with gradient properties can be produced. Finally, three hybrid cubes have been success fully fabricated by controlling FFF process and the flow rate of the foamable filament containing 4 wt.% of TEMs for different cases.