WooCommerce total cart volume (dimensions)

I’ve seen some people talking about displaying the total cart weight, but I’m hoping there’s a way to display total cart volume with WooCommerce?

The site sells products in shipping containers, and I need a way to display the total cubic volume of an order on the cart page, so that customers can ensure that it falls within one of two container sizes by adjusting the number of products in their cart.

I’m guessing I could use a custom product attribute to add the volume in cubic meters to each product, so all I would need is something basic to add up the total volume of the products in the cart.

The price doesn’t vary – there’s no shipping costs – it just needs to be a visual display.

Ideally, I would also like to display the total volume elsewhere on the site (along with the cart widget), so that customers can quickly check the volume of their order without going to the cart page.

Any help much appreciated!