You Do Need power plug adapter while traveling from Cocos (Keeling) Islands to Italy.

Here is Why You Need An Adapter

The outlet and plug type used in Italy are C, F and L and in Cocos (Keeling) Islands is I. This is how they look like.

Cocos (Keeling) Islands

In Cocos (Keeling) Islands, outlets of type I are in use.

Type I

Italy

In Italy, outlets of type C, F and L are in use.

Type C

Type F

Type L