An electric and hydraulic machine includes a housing defining a motor chamber and a pump chamber, a motor comprising a rotor and a stator positioned within the motor chamber, and a pump comprising a pumping element positioned within the pump chamber, the pumping element movable by the motor to displace fluid in the pump chamber. The pump chamber includes a low-pressure chamber and a high-pressure chamber, a unit inlet defined by the housing and in communication with the low-pressure chamber, and a unit outlet defined by the housing and in communication with the high-pressure chamber. The pump chamber is positioned radially inward of the motor chamber such that the pump is nested within the motor. A radial cooling channel extends in a radial direction from the low-pressure chamber to the motor chamber such that fluid in the pump chamber communicates with the rotor and the stator to cool the motor.