you're wrong; L3 is just an extension of L2 cache. It supplies information to the processor if it does not exist in L1 or L2. If L3 cache does not have the information then the process slows right down to RAM memory speed.
You are wrong to say "you're wrong"
Depends on the processor architecture, but most often, each block of L2 cache is dedicated to a core, while the L3 is shared across all the cores in the CPU. It makes a difference if you have multiple cores working the same data.