New Mexico is about 22,451 times bigger than Cocos (Keeling) Islands.

Cocos (Keeling) Islands is approximately 14 sq km, while New Mexico is approximately 314,310 sq km, making New Mexico 2,244,971% larger than Cocos (Keeling) Islands. Meanwhile, the population of Cocos (Keeling) Islands is ~596 people (2.1 million more people live in New Mexico).
Tip: This to-scale comparison of Cocos (Keeling) Islands vs. New Mexico uses the Mercator projection, which distorts the size of regions near the poles.