Type-C cables must include CC lines, so they all support USB-PD communication. Not all Type-C cables support the full range of power capabilities that USB-PD specifies, however.
The major differentiation is supported current. Passive Type-C cables support up to 3A by default at any USB-PD voltage range (standard voltages for fixed sources are 5V, 12V and 20V). So passive cables can carry up to 15W at 5V, 36W at 12V or 60W at 20V, if the source and sink negotiate an explicit contract for these voltage/current levels.
In order for a USB-PD compliant source to advertise capabilities greater than 3A (or up to the full 5A limit of the spec) the Type-C cable must be an Electronically Marked Cable Assembly (EMCA) and support SOP' packets. It must respond to the "Discover Identity" VDM sequence (USB-PD spec section 184.108.40.206.1) with a cable VDO packet with bits 6..5 set to indicate 5A current handling capability.