Why bode plot of cascade system is not the sum of subsystems?
If your question is about the phase plot, then note that 0deg phase is same as 360deg phase. You can add or subtract multiples of 360 deg to phase diagram without changing the physical meaning (conditions apply).
In the plots, the phase is not restricted to either (+0, +360) or (-180, +180). That may be why it doesn't look like addition. If it is matlab, right click to get to properties window and deselect unwrap phase option and check again.