Assuming the Core works like an Essence or BS2, you can put your Core and Chromecast audio into a "group" and cast Spotify to both of them.  You still need the Spotify app to control the music, but the music is sent directly to the devices rather than from the phone to the devices.  

In my experience, though, this tends to be a little fiddly.  Maybe every other time I try to use my Chromecast, I need to reset it, or my phone or both to get it to work.  It also tends to become uncontrollable after some time - that is, it will continue to play, but stop responding to commands from the app.  This seems to happen more frequently when I'm casting to a group.  I haven't experienced this with my Essence or BS2.  I thought it might be my network, but after upgrading to a mesh, I'm still having the occasional problem (and my other wifi related issues have disappeared).

It seems like some on this forum have no issues with the Chromecast, but I know I'm not alone... for $40 device, we live with it.