Okay, where did you take history? There was never a war between Spain and Mexico that was won by Spain. The only conflict between Spain and Mexico was the original revolution in which Mexico gained its independence; obviously Mexico won since they are in fact independent.
Further, the war in 1846 was between the US and Mexico; Spain had NOTHING to do with that war. Mexico was an independent nation by that point. It was a border dispute in Texas, along with lingering resentment on Mexico’s part over the annexation of Texas by the US that led to this war. This was the war that resulted in MEXICO turning over the territory that now comprises the American southwest. Spain did not control that territory by the time of the Mexican war, so there was no way that Spain could have ceded the territory to the US.
Spain and the US did fight a war, mainly over the Spanish treatment of Cuba and the rebels fighting against Spanish control of the island. However, that occurred in 1898, long after control of the southwestern states passed to the US. The only territory ceded by Spain to the US was Florida, back in the early 19th century and some Pacific island territories, most notably the Phillipines as a result of the Spanish-American war.
The Spanish were in California and other western states, Mexico was not, the US got the land from Spain.
Then in 1821 the upper classes in Mexico felt threatened by the Revolution of 1820 in Spain and the promise to restore the Constitution of 1812, and proclaimed independence. They were willing to recognize Ferdinand VII as their sovereign but the Spanish government rejected that, so the creole general Agustin Iturbide, who had earlier fought on the royalist side, made himself emperor of Mexico.