You Do Need power plug adapter while traveling from Nauru to Canary Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Canary Islands are C, E and F and in Nauru is I. This is how they look like.

Nauru

In Nauru, outlets of type I are in use.

Type I

Canary Islands

In Canary Islands, outlets of type C, E and F are in use.

Type C

Type E

Type F