This study reports fully 3D-printed, three-dimensional, soft magnetic-cored solenoids that generate three times the largest magnetic fields previously reported from 3D-printed solenoids. The devices are fabricated on a customised, multi-material 3D printer that can extrude both filaments and pellets. Three different kinds of materials are employed to manufacture the reported soft magnetic-cored solenoids: pure PLA (dielectric portions), PLA doped with copper particles (electrically conductive structures), and nylon or PLA doped with metallic particles (soft magnetic cores). Via manufacturing optimisation, the reported devices are 33% smaller and can withstand about twice the current, generating three times more magnetic field. The 3D-printed solenoids generate Gauss-level magnetic fields while drawing tens-of-milliamps currents and can be readily used to implement fully 3D-printed induction sensors. The results of this work extend the state of the art in 3D-printed electronics, enabling the creation of more complex and capable solenoids for in-situ manufactured and in-space manufactured electromagnetic systems.