The last nuclear bomb tested was on January 6 of this year, by North Korea.

Presumably though you mean by the Cold War superpowers. The US tested its last nuclear weapon underground on September 23, 1992. The Soviet Union/Russia tested its last weapon underground on October 24, 1990. The UK tested its last test in 1991, France in 1996, China in 1996. India and Pakistan most recently tested in 1998. Israel is not known for sure to have ever tested but may have had a clandestine test in 1979. North Korea is the only state that has tested nuclear weapons in the 21st century.

They were not tested merely as shows of power. They were tested to learn about the effects of the weapons and to advance knowledge in developing and using the weapons.

The states that did the most testing, the two major superpowers, agreed to a voluntary moratorium on testing at the end of the Cold War. The idea was explicitly to slow further development of nuclear weapons, as a marker of decreased tensions. There are still subcritical nuclear tests (which are tests that don't involve the substantial release of nuclear energy, but involve nuclear weapons components). The US and Russia have continued to work on the delivery vehicles (e.g. rockets, bombers) associated with nuclear weapons, but not the warheads themselves (except in ways related to their long-term maintenance).