The objective of this study was to assess the cellulase production of four fungi: Aspergillus terreus NIH2624, Aspergillus clavatus NRRL1, Aspergillus versicolor CBS583.65 and Aspergillus phoenicis ATCC3157, under submerged cultivation conditions. When these fungi were cultured in shake flasks using Mandels and Weber’s minimal medium with 1% sugarcane bagasse as a carbon source and 1.8 g/L of rice bran extract as a nitrogen source, A. terreus showed maximum cellulase production (filter paper activity (FPase) 3.35 U/mL; carboxymethyl cellulase activity (CMCase) 1.69 U/mL). Consequently, A. terreus was selected for the optimization study for cellulase production. Among the different tested carbon sources, A. terreus showed higher CMCase activity when it was cultivated on delignified sugarcane bagasse (1.64 U/mL) and higher FPase activity on sugarcane straw (7.95 U/mL). Regarding the nitrogen sources, the maximum FPase activity was observed when using rice bran (FPase, 8.90 U/mL) and soybean meal (FPase, 9.63 U/mL). The optimized fermentation medium (minimal medium with delignified sugarcane bagasse and rice bran as carbon and nitrogen sources, respectively) resulted in an enzymatic cocktail mainly composed of xylanases, with a maximum activity of 1701.85 U/mL for beechwood xylan, 77.12 U/mL for endoglucanase and 21.02 U/mL for cellobiohydrolase. Additionally, the enzymatic cocktail showed efficient activities for β-glucosidase, β-xylanase, arabinofuranosidase and lytic polysaccharide monoxygenases (LPMOs). This cellulase enzyme solution has the potential to efficiently hydrolyze lignocellulosic biomass, producing second-generation sugars in biorefineries.