A cementitious composite and cured masonry block made from the cementitious composite. The cementitious composite contains a cement, a non-rubber aggregate, a crumb rubber and at least one of cement kiln dust and limestone powder. The crumb rubber aggregate is extracted from scrap tires after being processed and then mixed in specified percentages with the aggregate, the cement and water, then cured in forms to make the masonry blocks. In the present disclosure sand, which is used in conventional masonry blocks, is at least partially replaced with crumb rubber to produce a sand-free or sand-reduced masonry block that contains crumb rubber. The crumb rubber masonry blocks satisfy the ASTM non-load bearing requirements. The use of crumb rubber decreases the unit weight and increases thermal resistance of the masonry blocks. The use of cement kiln dust or limestone as a partial replacement of cement will lead to decrease in the cost. The use of industrial waste materials, such as crumb rubber, limestone powder and cement kiln dust, will lead to economic and environmental benefits.