measure cache meory allocation

I'm facing an homework where I should "fill the register inside the CPU using C++".

While I understand that a single register should be once or twice the word size of the system and the L1 cache should be several dozens kilobytes, I don't understand how I should show that that space has been used up. Also, the flag "register" isn't even a command, it's more similar to a suggestion that the compiler manages as deemed necessary..

So far, I have written two snippets of codes that sum up the scenario that would produce bad allocation of cache memory: an over-sized array flagged as "register" and an infinite recursion which at every iteration allocates memory for a local variable flagged as "register".

I planned to place this code as examples and add an English explanation of the processes involved.

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Is there a way to measure the details of the registers/cache memory allocation in a program?