Magnetic hyperthermia treatment requires biocompatible magnetic nanoparticles with improved heating capacities to become a viable clinical method for cancer treatment. Although small superparamagnetic iron oxide nanoparticles under low fields have been favored (linear response theory regime), these nanoparticles present a series of limitations, including relatively low heating efficiency (specific absorption rate or SAR), that need to be overcome to make magnetic hyperthermia an efficient clinical application. We here show that by modifying the shape into deformed cubes (octopods) and tuning their size, their SAR can be greatly increased up to 70% (from 140 to 240 W/g). By using nonhydrolytic thermal decomposition, we have obtained highly crystalline monodisperse nano-octopods for different sizes (17-47 nm), and their heating response has been extensively studied in a wide range of AC fields (20-800 Oe) using combined calorimetric and AC magnetometry experiments. Our results consistently reveal that at AC fields (≤300-400 Oe), the nano-octopods with the smallest size (17 nm) possessed the largest SAR, but for higher AC fields (>400 Oe) the SAR tended to increase with increasing particle size, reaching maximum values up to 415 W/g for the 47 nm octopods. The different response has been attributed to the ratio between the applied field and the anisotropy field, which activates different heating mechanisms: mainly related to viscous losses in the case of the smallest nano-octopods, while mostly attributed to hysteresis losses in the case of the biggest ones. Our study provides important insights into the size-dependent SAR in anisotropic nanoparticles, other than what has been predicted by the linear response theory for the case of spherical nanoparticles, and paves a new pathway for the design and synthesis of novel anisotropic iron oxide nanostructures with optimal heating efficiency for enhanced hyperthermia.