Strong correlations exist between supermassive black holes (SMBHs) and their host galaxies. These correlations suggest a missing component in our current understanding: the role of energy cascade in SMBH-bulge coevolution. In this picture, energy is continuously cascaded from bulge scale $r_b$ down to the BH scale (Schwarzschild radius $r_s$). Energy cascade has a scale-independent, but decreasing rate $\varepsilon_b(t)\approx \sigma_b^3/r_b$ due to the cooling of baryonic component, where $\sigma_b$ is bulge velocity dispersion. The bulge mass-size ($M_b$-$r_b$) relation can be expressed as $M_b \propto \varepsilon_b^{2/3}r_b^{5/3}G^{-1}$, or a bulge density-size relation $\rho_b \propto \varepsilon_b^{2/3}r_b^{-4/3}G^{-1}$, with $\varepsilon_b \approx a^{-5/2}\times 10^{-4}m^2/s^3$, as confirmed by the galaxy survey, where $a$ is the scale factor and $G$ is the gravitational constant. Intermediate length scales can be defined based on the dominant physics on that scale, i.e. the BH sphere of influence $r_B$, radiation scale $r_p$, and dissipation scale $r_x$. For SMBH with a mass $M_B$, bolometric luminosity $L_B$, energy cascade leads to a "cascade" force that must be balanced by the BH radiation force in its early life, i.e. $L_B/c=M_B \varepsilon_b /\sigma_p$, where $c$ is light speed and $\sigma_p$ is the velocity dispersion on scale $r_p$. Since $\varepsilon_b$ is much larger in the early universe, BH accretion can be super-Eddington with $L_B$ exceeding the Eddington limit. In addition, the BH mass-dispersion relation ($M_B\propto \sigma_b^5$) is a natural result of the cascade theory. By introducing two dimensionless parameters $\gamma={L_B}/(M_B\varepsilon_b)$ and $\eta=({GL_B}/{c^5})^{{1}/{4}}$, the distribution and evolution of SMBHs can all be mapped onto the $\gamma$-$\eta$ plane. By setting $r_s \le r_p\le r_B$, the upper limit of distribution is found to be $L_B \propto (\varepsilon_b M_B)^{4/5}G^{-1/5}c$. The lower limit is found to be $L_B \propto (\varepsilon_b M_B)^{4/3}G^{1/3}c^{-5/3}$. Quasars tend to approach the upper limit, while dormant SMBHs (Sgr A* and M31) tend to approach the lower limit. A three stage mathematical model is proposed for SMBH evolution involving co-evolution, transitional, and dormant stages, respectively. Models are finally compared against the BH accretion history from quasar luminosity function from 2dF Redshift Survey, local galaxy and SMBHs data, and high redshift quasars from SDSS DR7 and CFHQS surveys.