Simple answer is yes you can grow sugarcane in New Zealand. Just have to be careful where you plant it, it needs plenty of sunshine to grow 

May is the traditional month when new seasons strawberry plants become available in New Zealand. The nurseries that grow the plants lift them once the autumn rains have moisten the soil sufficiently and they are then distributed to garden centres.

Some of the best places to buy seeds is Bunnings, Miter 10 and the Wearhouse.