Eight is what comes after a seven that has been treated as complete, and traditions that use it that way mean beginning again on a higher turn rather than simply adding one.
Jewish practice circumcises on the eighth day, and the festival of Hanukkah runs for eight nights. Early Christian writers made the eighth day the day of resurrection, standing outside the week as the first day of a new creation, and built baptisteries on an octagonal plan for exactly that reason. A reader who notices that so many old baptismal fonts have eight sides is looking at a doctrine in stone.
Chinese thought counts eight trigrams, the bagua, arranged around a centre in two classical orders and forming the basis of both the Book of Changes and the practice of siting buildings. Popular tradition has eight immortals, and in modern Chinese usage the number is lucky because the word for eight resembles the word for prosperity, a homophone effect that has driven the prices of number plates and telephone numbers.
Buddhism has the noble eightfold path and the eight auspicious symbols. Islam speaks of eight bearing the Throne on the day of judgement, and later tradition counts eight gates of paradise against seven of hell, an asymmetry read as mercy exceeding punishment.
For the Greek arithmologists eight was the first cube, three dimensions of two, and therefore associated with solidity in a literal geometrical sense before any moral one.