How can I change all IPs in my account to a different IP?

I have about 80 sites in my Cloudflare free account, and a couple in Cloudflare Paid. Almost all of these sites have DNS settings pointing to a server’s IP. We’re about to change servers, which means I’ll need to change the IPs for all our sites.

Instead of going through each site and DNS setting one by one, is there a way I can update my entire account in bulk? Can I say that anywhere the previous IP appears to change it to the new one?