  Using Exact Renormalization Group Equation approach and background field
method, we investigate the one-loop problem in a six-dimensional conformal
gravity theory whose Lagrangian takes the same form as holographic Weyl anomaly
of multiple coincident M5-branes. We choose the backgrounds to be the symmetric
Einstein spaces including S6, CP3, S2 \times S4, S2 \times CP2, S3 \times S3
and S2 \times S2 \times S2. Evaluating the functional sums gives power-law and
logarithmic divergences. We extract from the specific values of logarithmic
divergence on above backgrounds, the coefficient in front of Euler density and
two linear equations constraining the coefficients in front of three type-B
conformal invariants. As a test of the effectiveness of Exact Renormalization
Group Equation approach to quantum conformal gravity, we reexaminethe one-loop
problem in four-dimensional conformal gravity and confirm the logarithmic
divergence derived from generalized Schwinger-DeWitt method.
