Sending a Parcel

The Post Office used to have a strange way of limiting the size of parcels. The maximum allowed was "$6$ feet combined length and girth". That meant you added together the distance round the middle of the parcel (that's the girth) and the length.



I used to imagine sending a fishing rod very nearly $6$ feet long and just a few inches round the girth!

This problem is more up-to-date:

We will call the maximum combined length and girth $2$ metres (which is a bit more than $6$ feet).
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are $2$ metres and measurements are all made in whole centimetres?