The dimensions of ( B ^ 2 μ _ 0 ) will be (if μ _ 0 : permeability...

Energy density in magnetic field is given by $u = \dfrac{{B}^{2}}{2{\mu}_{0}}$. Therefore, dimensions of $\dfrac{{B}^{2}}{{\mu}_{0}}$ will be equal to the dimensions of energy per unit volume.

\left[\dfrac{{B}^{2}}{{\mu}_{0}}\right] = \left[u\right] = \dfrac{\left[{ML}^{2}{T}^{- 2}\right]}{\left[{L}^{3}\right]} = \left[{ML}^{- 1}{T}^{- 2}\right]