  We examine the interaction between massless scalar fields and the
gravitational field generated by a black hole solution that was recently
obtained in the consistent well-defined 4-dimensional Einstein-Gauss-Bonnet
gravity with a cosmological constant. In order to do this, we calculate
quasibound state frequencies of scalar fields for the spherically symmetric
black hole in the consistent 4-dimensional Einstein-Gauss-Bonnet-de Sitter and
Anti-de Sitter theories. The expression for the quasibound states is obtained
by using the polynomial condition associated to the Heun functions, and their
values are overdamped. We also demonstrate the stability of the systems.
