What is the legal test for a defendant to challenge his sentence under the Eighth Amendment of the United States?

'considerable burden' to show the sentence is disproportionate to his level of culpability. [Citation.] Therefore, '[f]indings of disproportionality have occurred with exquisite rarity in the case law.' " (People v. Em (2009) 171 Cal.App.4th 964, 972.)

The Eighth Amendment, which applies to the states through the Fourteenth Amendment to the United States Constitution, prohibits cruel and unusual punishments. It "contains a 'narrow proportionality principle' that 'applies to noncapital sentences.' " (Ewing v. California (2003) 538 U.S. 11, 20.) The Eighth Amendment " 'does not require strict proportionality between crime and sentence. Rather, it forbids only extreme sentences that are "grossly disproportionate" to the crime.' " (Id. at p. 23.) As with claims under our state Constitution, in determining whether a sentence violates the federal constitutional guarantee against cruel and unusual punishment, a court may consider "the gravity of the offense and the harshness of the penalty." (Solem v. Helm (1983) 463 U.S. 277, 292.) "Outside the context of capital punishment, successful challenges to the proportionality of particular sentences [under the federal Constitution are] . . . exceedingly rare." (Rummell v. Estelle (1980) 445 U.S. 263, 272.)