In his initial e-mail, Cuban, who is of Russian-Jewish descent, asked Facebook why these groups were allowed to exist when the company's Statement of Rights and Responsibilities says users will not post content that is "hateful" or "threatening." He also pointed out that in some European countries, speech denying the Holocaust is illegal.
He said he received a "canned corporate response" from Facebook saying only that they know it's a controversial content but they don't take down content simply for being controversial.
Cuban didn't revisit the issue until President Obama condemned Holocaust deniers at a Holocaust remembrance ceremony in late April.
He wrote about Obama's remarks and his Facebook concerns, and then posted them on his blog.
"That's when all hell broke loose," he said, adding that it prompted scattered media reports, blog posts and Twitter commentary.
In his open letter to Facebook's CEO Mark Zuckerberg, Cuban took the site to task for supporting groups that promote hatred and not being transparent about the process it uses to remove content.
"I want an affirmative statement from Facebook that these groups will not be tolerated. Whether it's a group of 1 or 1000, hate is hate and hate begets hate," said Cuban.
And Cuban and others point out that this is not a First Amendment matter but, rather, a corporate responsibility issue.
"Facebook is not a state actor. Its activities do not implicate the First Amendment," said Ryan Calo, a legal fellow at Stanford Law School's Center for Internet & Society. "Facebook has a Terms of Service and that could prohibit all kinds of different activities. It doesn't obligate Facebook to take stuff down. It just says [they] could."
He said the company is free to devise its own policies for what kinds of content are allowed to remain on the site. But Calo added that based on what Facebook has taken down, it appears that the company is looking to the First Amendment to frame the issue.
"If you want to draw a dividing line, you can constitutionally make it illegal when people are inciting violence," he said, adding that although the line is fuzzy, images and speech that approach obscenity are also not protected by the First Amendment.
Earlier this month, Facebook shut down a group called the "Isle of Man KKK," which urged members to keep the Island "free from foreigners" and included a picture of a hooded Ku Klux Klan member.
In an interview with CNN, Schnitt said the company removed the group because it interpreted the page as threatening and inciting violence.
In January, the company provoked mothers across the country, when it took down photos of women breast-feeding, citing its policy against nudity. Schnitt said the vast majority of breast-feeding photos are still on the site.
As the site continues to grow by leaps and bounds -- it's about 200 million members strong and adds about 3.5 million new users each week -- human and civil rights groups hope Facebook will revisit the way it monitors user activity.
"Hate on the Internet is growing like wildfire," said Deborah Lautner, director of civil rights for the Anti-Defamation League. In the past year, she said ADL has seen a 100 percent increase in the number of complaints from the community about hate speech online.