A machine and method of extruding concrete building product, e.g., brick, tile, paver, or shingles, and concrete mixture therefor. The mixture has aggregate, liquid and binder that includes fly ash and can include slag with moisture content controlled producing a zero or negative slump loose feed mixture compacted in a consolidation chamber of the machine into increased density consolidated mixture extruded from an extrusion chamber in communication with the consolidation chamber with compaction force being generally transverse to extrusion force. Compaction force is maintained during extrusion through a die of non-tapering construction. Where the extruded product is a brick, the extruded slug is cut into a plurality of bricks using a rotary cutter having an offset forming an increased moisture absorbing region in the cut surface of each brick formed from the slug that better bonds with mortar during bricklaying.