The cycle of power was from Spain to Mexico to Texas. US got hold of Texas in 1845 only.
Explanation:
From the given years here:
In 1810 Spain was in possession of the whole territory of Mexico including Texas.
After the Mexican war of independence the Mexicans were able to get the control of Texas in 1821 but that was not to be for long.
After only a few years Texas started seceding and then eventually declared itself into an independent country.
So to summarize:
1810 onward: Spain
1821 onward: Mexico
1826: Texas
US only ruled Texas from 1845 which is not a part of the given timeline.
