I just received my new Apple IPad. The charger uses a USB-C to USB-C cord. Can I order a USB-A to USB-C cord so I can use the charging cubes that I already own?

Yes, with the correct cable, you can use your existing Power Adapters.

Here is one of the better USB-C to USB Type-A cables marketed by Apple:

mophie USB-A Cable with USB-C Connector (1 m)

https://store.apple.com/uk/xc/product/HN892ZM/A

I couldnt’t find a USB A to C charging cable (may not have found it) but I did find a USBC to Lightning which could allow you to charge your older devices with your newer power block (if that’s what you’re trying to do, use one block for multiple devices)

https://www.apple.com/shop/product/MX0K2AM/A/usb-c-to-lightning-cable-1-m?fnode=cb5364ef3bcd9d8e87d1d2ff1707a16b12d7522abd6c8bf3a8d09fd7a956f261b1e468283238f138498cacc60f68453bd05ba0d2fff6437fae28887b63466a90009bcd5da6de47a22b3fcb6c6e8834ebe65b39a0381e9b4b0dfda736e246518cee5e51b7d63fe2490b8555d7394a4ecc&fs=f%3Dusb-usbc%26fh%3D4588%252B30a3%252B4891