Fourier coefficients of $\mathrm{Sp}(4)$ Eisenstein series

We compute explicit formulae for the constant terms and Fourier coefficients for Eisenstein series on Sp$(4,\mathbb R)$, in terms of zeta functions and Whittaker functions. We also develop a generalisation of Ramanujan sums to Sp$(4,\mathbb Z)$, which appear as coefficients in the Fourier expansion for the minimal Eisenstein series.