Hillary Clinton also weighed in on The Citadel college, where the Confederate battle flag flies, tweeting: "Symbols of hate create more hate. It's time for the Confederate flag to come down at The Citadel."
The flag was the focus of renewed impassioned debate in June after a suspected white supremacist shot dead nine black churchgoers in Charleston, South Carolina- the same city where The Citadel is based.
"Eight cadets have been suspended and went home this morning," Citadel spokeswoman Kim Keelor told AFP.
Retired Lieutenant General John Rosa, the academy's president, said the cadets had been singing Christmas carols as part of a "Ghosts of Christmas Past" skit.
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The photos, which were splashed across social media were "offensive and disturbing," he said in a statement, ordering an investigation.
"These images are not consistent with our core values of honor, duty and respect."
In a website attributed to him, accused Charleston church shooter Dylann Roof espoused racist views toward African-Americans and, in photos, posed with firearms and the Confederate flag.