  We derive from the subleading contributions to the chiral three-nucleon
interaction [published in Phys.~Rev.~C77, 064004 (2008) and Phys.~Rev.~C84,
054001 (2011)] their first-order contributions to the energy per particle of
isospin-symmetric nuclear matter and pure neutron matter in an analytical way.
For the variety of short-range and long-range terms that constitute the
subleading chiral 3N-force the pertinent closed 3-ring, 2-ring, and 1-ring
diagrams are evaluated. While 3-ring diagrams vanish by a spin-trace and the
results for 2-ring diagrams can be given in terms of elementary functions of
the ratio Fermi-momentum over pion mass, one ends up in most cases for the
closed 1-ring diagrams with one-parameter integrals. The same treatment is
applied to the subsubleading chiral three-nucleon interactions as far as these
have been constructed up to now.
