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 through 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 through 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.