Blocks for wall constructions described herein are in the form of casted one-piece concrete hollow bodies. The blocks include front and back walls which are generally parallel to a first axis and have top and bottom ends and two inner walls integral to both front and back walls therebetween that are generally parallel to a second axis which is perpendicular to the first axis. One of the end side faces of the two inner walls includes male connector portions that are offset from a first distance from the front wall. The other end side face includes female connector portions that are registered along the first axis with the male connector portions and are offset from the first distance from the back wall. The male connector portion is for insertion in the female connector portion of another block when the other block is mounted thereon so as to yield a straight or a shifted retaining wall portion. The shifted retaining wall portion results from the first and second blocks having their front walls on a same side relative to the first axis and the straight retaining wall portion results from the first and second blocks having their front walls on opposite sides relative to the first axis. Further embodiments of the blocks include further female receiving portions allowing versatile positioning of the blocks.
