The Fourier coefficients, in particular the constant terms, of Hilbert-Eisenstein series have the number theoretic importance. The value at a cusp gives the constant terms of the Fourier expansion centered at the cusp. We give the values at all the cusps equivalent to √-1∞, of some specific Hilbert-Eisenstein series whose Fourier coefficients of higher terms are in rather simple form. The result may be useful to obtain the special values of L-functions or to investigate the Shimura lifting for elliptic modular forms.