This is 羞恥心 (Shuuchishin) performing their song um..羞恥心 (Shuuchishin).
(thanks to youtube user iideainet)
The song is used as the ending theme to the show that the three members of Shuuchishin regularly appear on, クイズ!ヘキサゴンII (Quiz Hexagon II). The three members, Takeshi Tsuruno, Naoki Nokubo, and Yuusuke Kamiji are well-known on the show for being...well..morons. They regularly place at the end of the paper test that the contestants have to take before each episode and a lot the different events on the show are dependent on them and their female counterparts Yukina Kinoshita, Suzanne, and Mai Satoda being idiots who can't read, don't have any common sense, and are generally unfamiliar with things that regular Japanese people should know. I don't know most of the things that appear on the show but hey, I have an excuse. The six of them provide lots of unintentional comedy and give the host (whom I don't like and won't name) lots of opportunities to berate them for being morons.
The females actually had a single out first as the unit Pabo, 恋のヘキサゴン (koi no hexagon):
(thanks to youtube user justwanahvefun)
Koi no hexagon topped out at number 19 on the charts while Shuuchishin has gone as high as number 1 on the Billboard Japan charts.