Punishments can be either cruel or unusual. They just cannot be both.
In Furman v. Georgia, 408 U.S. 238 (1972), Justice Brennan wrote, "There are, then, four principles by which we may determine whether a particular punishment is 'cruel and unusual'."
* The "essential predicate" is "that a punishment must not by its severity be degrading to human dignity," especially torture.
* "A severe punishment that is obviously inflicted in wholly arbitrary fashion."
* "A severe punishment that is clearly and totally rejected throughout society."
* "A severe punishment that is patently unnecessary."
These "principles" probably themselves have oblique legal meanings seperate than what we'd expect, and there's probably been a new ruling or two on the 8th amendment in the past 41 years.
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[0] IANAL.
[1] Yes, I know.
Seems like bullshit. Cruel punishment does not become okay if you do it frequently.
The ban in the 8th amendment is on "cruel and unusual punishments". Therefore punishments that are cruel or unusual, but not both, are not banned.
For example it would be hard to argue that excessive prison time is at all unusual in this country. So no matter how cruel it may be, it passes muster. Conversely Shena Hardin was given the unusual punishment of having to stand on a particular sidewalk wearing a sign that said, "Only an idiot would drive on the sidewalk to avoid a school bus." (She was, in fact, said idiot.) The punishment was unusual, but not cruel. It therefore passed constitutional muster.
However being kept in an overly crowded prison without appropriate medical care qualifies as both cruel and unusual punishment and is therefore unconstitutional. (As a variety of courts have had to repeatedly point out to California. Personally I'd love to see the fraction of the prison population that is over the design capacity of prisons in California become the portion of the year that key officials should have to spend inside of said prisons. I'm sure that we'd see Jerry Brown stop dragging his feet on the issue fairly promptly...)
See http://www.constitution.org/eng/eng_bor.htm for the full bill in question.
That Cesare Beccaria's comments could have given the idea more force I can believe. But they are not the source. Nor am I aware of any court case that has specifically discussed Cesare Beccaria for trying to understand this clause. By contrast search https://supreme.justia.com/cases/federal/us/501/957/case.htm... for comments about Titus Oakes (the historical cause of that clause).
Punishments are PERMITTED to be either cruel, or unusual. But not both.