Inhomogeneous quadratic forms and triangular numbers

We prove an explicit formula for the number of representations of an integer as the sum of n triangular numbers for each n in the range 2 ≤ n ≤ 8 as special cases of a more general formula applicable to an inhomogeneous quadratic form over a totally real number field. The formula can be derived by calculating explicitly the Fourier coefficients of a certain Eisenstein series that appears in the Siegel-Weil formula for an inhomogeneous quadratic form.