Talents
Music
Cartman appears to be very musically talented. He plays the piano quite well in the episode "Christian Rock Hard," the violin in "Something Wall-Mart This Way Comes," the French horn in "Summer Sucks," the drums in "The Red Badge of Gayness," the harmonica in "Jakovasaurs," the recorder in "World Wide Recorder Concert," and the acoustic guitar in "Chinpokomon." Cartman frequently bursts into song, often spontaneously. This penchant for ad hoc songs was specifically mentioned in "Ginger Kids". His Christian rock group "Faith + 1" sold 1,000,000 copies of its album in the episode "Christian Rock Hard." In the film South Park: Bigger, Longer, Uncut, Cartman is shown singing in Chinese, French, Dutch and an unidentified African language. In "Mr. Hankey's Christmas Classics", Cartman sings, "O, Holy Night" (despite several interruptions). In Chef Aid, he sings and does a German dance to raise money for Chef's legal fees. This same episode shows for the first time that Cartman has the uncontrollable urge to finish singing "Come Sail Away" by Styx whenever he hears any part of the song, which he can do, under pressure, in 27 seconds. Also note that he can dance with the other boys in his dream of Fingerbang's fame in Something You Can Do With Your Finger.
Manipulation and leadership ability
Although having his origins as little more than a comic foil, Cartman has evolved into a character of stunningly articulate manipulative talents, following closely in the footsteps of other famous manipulators such as the character Iago from William Shakespeare's Othello. In several episodes throughout the series, he employs this skill to get what he wants. His most frequent targets are Butters and adults in general, including convincing Butters to "take one for the team" and be anally pack raped by men from NAMBLA in Cartman Joins NAMBLA. He was able to get Congress to lift the ban on stem-cell research in the episode "Kenny Dies" and talked the ginger kids out of killing all non-gingers after Kyle told him that they had played a trick on him in "Ginger Kids". Earlier in that episode he had rallied all the gingers to exterminate all non-gingers in a Hitler-esque way. In the episode "Tsst", Cartman was able to drive several nannies from his house with insults and insinuation (even causing one to be put in a mental home).
Cartman's perceived stupidity by his friends can be attributed to his sometimes naive behavior, however his uncanny skill at manipulation, bilingualism, and ability to create elaborate schemes which are often effective imply a suprisingly high intellect. Cartman seems to have no problem talking to people and speaking in general. He has an uncanny way with words and uses that to his advantage whenever he plots an idea. For example, in episode: "Kenny Dies," Cartman delivers a speech to the United States House of Representatives convincing them to vote in favor of stem cell research. He also appears to be multilingual. He claims to be able to speak Spanish in Rainforest Schmainforest, and in My Future Self n' Me, he actually speaks Spanish to the Mexican workers hired to smear Butter's home with excrement. In D-Yikes Eric Cartman again demonstrates his proficiency in Spanish when hiring Mexicans to write an "essay" on The Old Man and the Sea. In the Passion of the Jew Cartman can speak (badly pronunced)German.
In "Cartoon Wars", he exploited a controversy involving the appearance of Muhammad on FOX's Family Guy to try to get the show off the air; he pretended to be the hapless victim of an Islamic terrorist attack to try to discourage the FOX president and the Family Guy staff writers from airing the Muhammad episode. On another occasion he was able to convince the majority of the adults of South Park to nearly take over the U.S. via an out-of-hand re-enactment of the Civil War, as long as he kept them drunk so they wouldn't realize what they were doing.
Cartman's shining accomplishment (according to Comedy Central's list of "Cartman's 25 Greatest Moments") came in the episode "Scott Tenorman Must Die." Though Scott Tenorman continually defeats Cartman throughout the episode, Cartman has the last laugh as he indirectly coerces Scott's parents into a situation where they are trespassing, and are consequently shot and killed. Cartman then steals the bodies and makes them into a chili which he promptly feeds to Scott. To make matters worse, Tenorman's favorite band, Radiohead, whom Cartman had arranged to be there so that they would be at the scene just as Scott had found out about his parents' deaths, sees him crying over the loss of his parents and deems him a cry baby. Cartman laughs hysterically at the inconsolable Tenorman, licking the tears from his face and dubbing them 'the tears of unfathomable sadness'.