The energy associated with electric field is (U_E) and with magnetic fields is (U_B) for an electromagnetic wave in free space. Then

Average energy density of magnetic field,

${\mathrm{u}}_{\mathrm{B}}=\frac{{\mathrm{B}}_0^2}{4{\mathrm{\mu }}_0}$
Average energy density of electric field,
${\mathrm{u}}_{\mathrm{E}}=\frac{{\mathrm{\epsilon }}_0{\mathrm{E}}_0^2}{4}$
Now, E₀ = CB₀ and 
${\mathrm{C}}^2=\frac{1}{{\mathrm{\mu }}_0{\mathrm{ϵ}}_0}$
$\begin{array}{l}{\mathrm{u}}_{\mathrm{E}}=\frac{{\mathrm{\epsilon }}_0}{4}\times {\mathrm{C}}^2{\mathrm{B}}_0^2=\frac{{\mathrm{\epsilon }}_0}{4}\times \frac{1}{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0}\times {\mathrm{B}}_0^2=\frac{{\mathrm{B}}_0^2}{4{\mathrm{\mu }}_0}={\mathrm{\mu }}_{\mathrm{B}}\\ \therefore {\mathrm{u}}_{\mathrm{E}}={\mathrm{u}}_{\mathrm{B}}\end{array}$
Since energy density of electric and magnetic field is same, so energy associated with equal volume will be equal i.e. ${\mathrm{u}}_{\mathrm{E}}={\mathrm{u}}_{\mathrm{B}}$