How much did the United States pay for New Mexico and California?

The lands in question were mostly gotten as a result of the Mexican-American War, and the settlement called for a $15 million payment to Mexico (but most of it was simply pro-rated out of Mexico's war debt). The Southernmost portions of Arizona and New Mexico were part of a later arrangement, the Gadsden Purchase, which involved$10 million in cash.

It gets a little complicated to determine how much of the money went toward paying for those two states because, even before gold was discovered there, California and New Mexico made up less than half of the lands involved.

In America's defense, however, Mexico only held those lands for about twenty years (after independence from Spain) and made little effort to settle or manage them, so the "It's part of Greater Mexico/Azatlan" arguments ring a little hollow too. And Mexico ceded the lands at gunpoint during a very trumped-up war, so there's no clear "We bought it fair and square" argument to be made.