cw complex inclusion induces homotopy group isomorphism

Question

In Hatcher's Algebraic Topology, he proved the following result: For a path-connected CW complex $X$ the inclusion $X^1 \rightarrow X$ induces a surjection on $\pi_1$, and the inclusion $X^2 \rightarrow X$ induces an isomorphism on $\pi_1$. I am wondering whether there is an analogous result to higher homotopy group.