In case of CEF, if it is using cache memory to store the FIB table entries or it uses specialised hardware to store it. And for processing this if it uses router/switche's processor memory or it has specialised hardware to do this.
CEF routers ( like 2800,2900,3800,3900,...) doesn't have any special hardware to store the FIB table. It will be stored in the DRAM and it uses the CPU to switch the traffic.
Routes like 7600, GSR does hardware forwarding using hardware ASIC
In hardware switched boxes, the hardware switched packet doesn't need to go the route processor CPU
Raju explained very well about the CEF function and I would like to add few things with Raju.
*** Please rate if the post is useful ***