A Strange Computer : Cache based computer
The question does not contain enough detail AND the description is probably incorrect. 

"Cache" IS (in most cases you will meet) RAM which is controlled by the system rather than by the program directly. 

RAM is an acronym for "Random Access Memory" which means a "bank" of storage registers which the program can write to and read from as required under program control. For a computing system to do useful work it must be able to access and alter variable storage, which is what RAM is. 

Unless you redefine what "RAM" means conceptually then you cannot have a useful RAM-less computer.