Final answer:
The statement is false; multi-core CPUs do indeed have room for cached memory, with each core often having its own L1 and L2 cache, and possibly sharing a larger L3 cache with other cores.
Step-by-step explanation:
The statement is False. Multi-core CPUs actually do have room on them for cached memory. In modern processors, each core often contains its own dedicated L1 and L2 cache, and they may share a larger L3 cache with other cores. This cached memory is essential for the CPU's performance, as it provides fast access to frequently used data and instructions, which would otherwise have to be fetched from the slower main memory.
The cache on a multi-core CPU enables each core to quickly access data without having to wait for communication with the computer's RAM. This results in much better performance, especially in tasks that require quick data retrieval and processing. So, rather than not having room for cache, multi-core processors are designed to integrate cache as a key part of their architecture for maintaining high efficiency and speed.