Molecular calculations for the theological behavior of a melt of multiply branched polymers with three levels of branching are presented. Extending the Doi-Edwards-de Gennes tube model, we consider a relaxation hierarchy where the entangled chains relax from the outermost sections toward the center of a branched treelike molecule. Generalizing star-polymer dynamics gives relaxation times in linear response. By including stretching of segments, predictions are made for the stress in nonlinear response. Relative motion between tube and polymer chain is included in the orientation dynamics. The novel constitutive equation we propose predict characteristic features in the nonlinear theology. These features arise from coupling of the stretch and orientation in different sections of the molecule. Such coupling and relative tube-chain motion are not present in existing molecular theories yet may be significant in the theology of multiply branched polymers such as low-density polyethylene. The full tube-model calculation is compared to a "multimode pom-pom" model of the same architecture, illuminating the approximations made in that approach.