  Superpotentials (antisymmetric tensor densities) in Einstein-Gauss-Bonnet
(EGB) gravity for arbitrary types of perturbations on arbitrary curved
backgrounds are constructed. As a basis, the generalized conservation laws in
the framework of an arbitrary D-dimensional metric theory, where conserved
currents are expressed through divergences of superpotentials, are used. Such a
derivation is exact (perturbations are not infinitesimal) and is approached,
when a one solution (dynamical) is considered as a perturbed system with
respect to another solution (background). Three known prescriptions are
elaborated: these are the canonical N{\oe}ther theorem, the Belinfante
symmetrization rule and the field-theoretical derivation. All the three
approaches are presented in an unique way convenient for comparisons and a
development. Exact expressions for the 01-component of the three types of the
superpotentials are derived in the case, when an arbitrary static
Schwarzschild-like solution in the EGB gravity is considered as a perturbed
system with respect to a background of the same type. These formulae are used
for calculating the mass of the Schwarzschild-anti-de Sitter black hole in the
EGB gravity. As a background both the anti-de Sitter spacetime in arbitrary
dimensions and a not maximally symmetric "mass gap" vacuum in 5 dimensions are
considered. Problems and perspectives for a future development, including the
Lovelock gravity, are discussed.
