A structural insulated building unit is provided for constructing a building. The structural insulated building unit includes an insulating core, first and second cementitious panels, and a connecting portion. The insulating core is defined by multiple sides and opposing first and second faces. The first and second cementitious panels are coupled to the first and second faces of the insulating core. The connecting portion is provided on one of the sides of the insulating core, and aligns the structural insulated building unit with an adjacent structural insulated building unit having a complementary connecting portion when constructing a building.