  In the framework of ordinary-derivative approach, conformal gravity in
space-time of dimension six is studied. The field content, in addition to
conformal graviton field, includes two auxiliary rank-2 symmetric tensor
fields, two Stueckelberg vector fields and one Stueckelberg scalar field. Gauge
invariant Lagrangian with conventional kinetic terms and the corresponding
gauge transformations are obtained. One of the rank-2 tensor fields and the
scalar field have canonical conformal dimension. With respect to these fields,
the Lagrangian contains, in addition to other terms, a cubic potential. Gauging
away the Stueckelberg fields and excluding the auxiliary fields via equations
of motion, the higher-derivative Lagrangian of 6d conformal gravity is
obtained. The higher derivative Lagrangian involves quadratic and cubic
curvature terms. This higher-derivative Lagrangian coincides with the simplest
Weyl invariant density discussed in the earlier literature. Generalization of
de Donder gauge conditions to 6d conformal fields is also obtained.
