You Do Need power plug adapter while traveling from New Zealand to Cuba.

Here is Why You Need An Adapter

The outlet and plug type used in Cuba are A, B, C and L and in New Zealand is I. This is how they look like.

New Zealand

In New Zealand, outlets of type I are in use.

Type I

Cuba

In Cuba, outlets of type A, B, C and L are in use.

Type A

Type B

Type C

Type L