His earliest works tended to be non-political because he seems to have been sharpening and evolving his artistic skills until he reached his early 30s. He spent about a dozen years in Europe -- Paris, mostly -- starting in 1907, and knew many of the modernist artists who created the onslaught of stylistic "isms" in the early 1900s. This included Cubism, a practice he adopted for about three years, and the subject of this post.
Wikipedia's Rivera biography is here. A discussion of his Cubist phase can be found here. Rivera's Cubist paintings was the subject of a museum exhibit in Dallas a few years ago.
Here are some of Rivera's works from that period.
An example of Rivera's mature style. There are political implications here, but they are less overt than usual.
This image and the one above it have hints of Cubism, but are largely representational with other modernist elements thrown in. I like them better than his more purely Cubist works.
Cubist faceting is more prominent here, but use of "multiple perspectives" is still absent.
Now we find face-on and profile views, here for a portrait of a Russian artist. A muted Braque-Picasso color scheme also intrudes.
Many facets, but not much in the way of varying viewpoints. Apparently Rivera could do Cubism superficially, but had a hard time going all the way. Perhaps he realized that Cubism's central premise was silly in reality.
Another derivative experiment by Rivera. No worse than many Cubism-inspired painting of that time.
The subject is shattered Cubist-style, but the woman in the upper-left corner is garden-variety modernist.
The rifle is not cubified: Rivera's homage to revolutionary times back home in Mexico.
Plenty of facets and even some Fauvist coloring. Rivera abandoned Cubism not long after this painting was made.