Electromagnetic waves in a box:
$$\nu_i=n_i \frac{ c}{2L}$$
$$dn^3/L^3=\frac{8\pi}{ c^3} \nu^2 d\nu$$
Total number of oscillators:
$$\sum_{n=0}^{\infty} \exp\left(-n\frac{h\nu}{kT}\right)=\frac{1}{1-\exp\left(-\frac{h\nu}{kT}\right)}$$
Total energy:
$$\sum_{n=0}^{\infty} n{h\nu} \exp\left(-n\frac{h\nu}{kT}\right)=\frac{{h\nu}\exp\left(-\frac{h\nu}{kT}\right)}{
\left(1-\exp\left(-\frac{h\nu}{kT}\right)\right)^2}$$

Energy density distribution \(\left[\frac{J}{m^3}\right]\):
$$u(\nu,T)d \nu=\frac{8\pi \nu^2}{c^3}\frac{h\nu}{\exp\left(\frac{h\nu}{kT}\right)-1}d \nu$$
$$u_{\lambda}(\lambda,T)d \lambda=\frac{8\pi }{\lambda^5}\frac{hc}{\exp\left(\frac{hc}{\lambda kT}\right)-1}d \lambda$$
Radiation flux density \(\left[\frac{W}{m^2}\right] \):
$$I(\nu,T)d \nu=\frac{c}{4} u(\nu)d \nu =\frac{2\pi \nu^2}{c^2}\frac{h\nu}{\exp\left(\frac{h\nu}{kT}\right)-1}d \nu$$
$$I_{\lambda}(\lambda,T)d \lambda=\frac{2\pi }{\lambda^5}\frac{hc^2}{\exp\left(\frac{hc}{\lambda kT}\right)-1}d \lambda$$