Key visuals of Taiko no Tatsujin White ver. take the imagery of the Japanese creation myth, and with that comes a multi-artist song collection named the God Collection (ゴッドコレクション), drawing references from parts of Japan's prehistory and the Shinto culture's over eight million gods and deities (kami).
Let's get a very brief overview for the figures and concepts referenced in the four songs that are currently released under the name. If you want to know more, we would recommend you to go do your own research, which would be more fun anyway.
KUSANAGI
"Kusanagi" here refers to the Kusanagi-no-Tsurugi (草薙の剣), literally "sword that cuts/shaves grass". This sword is one of the three important Imperial Regalia/Sacred Treasures of Japan, together with the Yata no Kagami mirror and Yasakani no Magatama jewel piece.
カグツチ Kagutsuchi
Kagutsuchi (カグツチ, some hyphenates as Kagu-tsuchi) is a kami of fire from Shinto mythology. He was given birth by Izanami, who suffered severe burns in her body (especially the reproductive organs in some accounts) and ultimately dies from it. Izanagi, under tremendous fury and grief, beheaded and dismantled Kagutsuchi by blade, leading to more landforms and deities created.
黄泉のイザナミ Yomi no Izanami
We haven't touched on it when we mentioned them in the last section, but Izanagi (イザナギ) and Izanami (イザナミ) are two deities who together created a mass of multiple gods and island landforms of Japan, being siblings as well as a husband-wife couple. Following her death in the story from above, Izanami descended to Yomi (黄泉), the underworld. Izanagi ventured to Yomi to retrieve her but was in vain, because she ate the food there so she could not return to the land of the living. In curiosity he lighted a fire to see her in the darkness, but found her to have transformed into a pest-infested mass. In fear, Izanagi fled Yomi and blocked the entrance, locking Izanami inside. Izanami vowed that she will take 1000 lives a day for him leaving him, and Izanagi replied he will give life to 1500. This is why she is also considered the goddess of death.
Other cultural/historical references used in the song's lyrics include the setting of a descendant of Himiko, shaman-queen of Yamataikoku (see also Yamatai Night Party), and a close friend, significant quotes from Ooharae-no-kotoba, liturgy for cleansing ritual, and mentions of major Shinto deities Amaterasu and Susanoo-no-mikoto.