  Donagi and Markman (1993) have shown that the infinitesimal period map for an
algebraic completely integrable Hamiltonian system is encoded in a section of
the third symmetric power of the cotangent bundle to the base of the system.
For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and
Pantev. We prove that the Balduzzi--Pantev formula holds along maximal rank
symplectic leaves of the G-generalised Hitchin system.
