Any software of more than moderate complexity is impossible to fully test via blackbox testing. You can verify that for the inputs you tried it works - but without digging into the implementation you have no way to prove that although it works for Z, Y and X that it also will work for W (which may cross an internal boundary in the implementation). Exhaustive blackbox testing is usually impossible.
I remember once upon a time in high school (now a few decades in the past) that I solved a Calculus problem and got a numeric test case answer correct to 4 decimal places. My solution was wrong - I had by pure dumb luck picked a test case where my mistakes just happened to cancel out.
My numeric test case was blackbox testing. The whitebox testing of examining my actual solution was what told me that even though my test case passed, the problem solution was not correct.
Both have their place.
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