The invention discloses a blow moulding machine for producing a cubic container. The blow moulding machine comprises a machine frame, a screw extruder, a mould head, a mould clamping device, an air blowing device, a hydraulic system, a pneumatic system and a control device. The mould head comprises a mould head main body, a core shaft and a mould mouth mechanism. The mould head main body is internally provided with a storage bin. The mould mouth mechanism comprises a connecting ring, a mouth mould fixing sleeve, a mouth mould, a core mould, a flexible ring and a flexible ring limiting sleeve.The invention further discloses a working method of the blow moulding machine for producing the cubic container and comprises the steps of installing a mould head mechanism, extruding by the extruder,pushing to forming a designated parison, pre-blowing, mould clamping, blowing, mould removing and deflashing. According to the blow moulding machine, the mould mouth mechanism is changed, the flexible ring is pulled through a driving mechanism, and the flexible ring is stressed and deformed, so that billet flowing channels are formed between the core mould, the mouth mould and the flexible ring are deformed, parison positions corresponding to the eight top corners of the cubic container are deformed, radial clearance adjusting is achieved, the mass is lower, and disassembly and assembly are convenient.