Multiformat box forming machine which comprises, at least, a storage unit (1) for die-cut cardboard sheets (2), a loader (3) for unit-by-unit dispensing of the die-cut sheets (2), means (4) for guiding and positioning the die-cut sheet (2), means (5) for supplying an adhesive substance on the die-cut cardboard sheet (2), a shaping unit (6) which comprises at least a vertically displaceable inner mould and an exterior matrix, and means (9) for discharging the formed box (10). The mould and the matrix of the shaping unit (6) are divided into four segments, respectively, which allow horizontal displacement and positioning thereof at the points which coincide with the lower corners of the box (10), it having been provided that each one of the units of mould-matrix segments move solidly joined together.