Using the disc drive as scale instead of the controller.
Might be generous on the size, might not be, hard to say.
Xbox One Dimensions = 7208cm3 = 33.3cm x 27.4cm x 7.9cm
Xbox One S Dimensions = 4342cm3 = 29.5cm x 23cm x 6.4cm
Xbox One X Dimensions = 4320cm3 = 30cm x 24cm x 6cm
Xbox Series X Dimensions = 6180cm3 = 28.6cm x 14.7cm x 14.7cm (Drive as scale)
Xbox Series X Dimensions = 6570cm3 = 29.2cm x 15cm x 15cm (Controller as scale (XBO Dimensions))
With the new controller apparently being smaller it seems likely that the volume is between 6000cm3-6500cm3