  We prove an intrinsic Taylor-like formula for a class of Lie groups arising
in the study of some sub-elliptic differential operators, namely the Kolmogorov
operators. The estimate of the remainder is in terms of the intrinsic norm
induced by such operators. These results extend the recent developments in a
work by Pascucci and the present authors, where a full characterization of the
intrinsic H\"older spaces and their Taylor polynomials were given under the
additional assumption that the Lie group is homogeneous in the sense of Folland
& Stein. Remarkably, the intrinsic Taylor polynomial admits the same
representation as in the homogeneous case.
