I personally thought it was an obvious point of logic.

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...)

The 8th Amendment is based on Cesare Beccaria's On Crimes And Punishments and the term "cruel and unusual" specifically means the punishment should be proportionate to the crime.

I find this theory unlikely given that many sources and a number of US legal cases cite a clause of the English Bill of Rights of 1689 as the source. Said clause being, That excessive bail ought not to be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted;

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).

Doesn't this make various three strike laws unconstitutional?

I certainly think so, not to mention inhumane, fiscally irresponsible and in defiance of all evidence about how to craft an effective criminal justice system.

Do you have an example of a "cruel" punishment?

How about solitary confinement, the long term use of which is most clearly torture? This happens very commonly in the US for all manner of "disrespect of authority" in prison, usually over political matters (prison politics, not red v blue for whichever dummy was going to say that after this post).

Many punishments are cruel. Prison is cruel. So is death.

Ask the SCOTUS. It was their interpretation.

I think he meant:

Punishments are PERMITTED to be either cruel, or unusual. But not both.

I took it as an ironic comment.

The way I understand the comment is that a punishment has been deemed legal if it is cruel XOR unusual, but not both.