the invention relates to modular building blocks with the minimal possible number of types which can be used for construction of buildings or other structures . the block has cellular structure defined by though openings made in the block body . the number of cells depends on the number of through holes . each block has an upper and inner insert made of a heat / cold - insulation material and inserted into through openings of the hollow block . the inserts , in turn , have though holes and recesses arranged so that after the blocks with inserts are assembled into a building or a structure , the openings and the recesses in the inserts form a continuous lattice - like space suitable for pouring concrete or another hardenable material which after curing form a load - carrying lattice - like framework of the building or the structure . thus , the inserts are used as formwork elements for pouring the concrete . since the inserts are made of a soft heat / cold insulating material , they compensate for lateral forces developed during setting of the concrete and thus unload the inner and outer walls of the structure . the invention also relates to the method of construction and to structural elements and buildings erected by the aforementioned method from the blocks of the invention .