We have systematically investigated the spectroscopic properties in even-even 222-228Ra by introducing the cluster degrees of freedom within the coupled-channels method, which allows the core 208Pb to occupy the octupole 3-state (Calc. I), as well as both the octupole 3-and quadrupole 2+ states (Calc. II), along with multipole interactions. Excellent agreement has been achieved between our calculated results and available data on energy spectra, reduced electromagnetic E lambda transition-matrix elements, and intrinsic electric dipole, quadrupole, and octupole Q lambda moments, pointing to the existence of strong octupole correlations in this region. The description of parity-doublet bands and electromagnetic-transition properties in both calculations is consistent with each other and with experimental data, which confirms the reliability of the coupled-channels formalism based on the cluster-core configuration in heavy nuclei. The enhanced E2 and E3 matrix elements in both calculations for 222-226Ra suggest that these three nuclei can exhibit static octupole deformation in both positive-and negative-parity bands. On the other hand, the accurate reproduction of the higher negative-parity bandhead and the derived Q3 moments in nucleus 228Ra is consistent with the interpretation of this nucleus as a deformed rotor exhibiting dynamic/soft octupole vibrations. We hope that the present work may open new avenues for exploring octupole collectivity and cluster correlations in heavy nuclei.