Family and identity. These fanfics usually explore how the brother fits into the Saiyan family. Is he as noble as Goku? Or does he have a different view on their Saiyan heritage? It's all about self - discovery.
Another common theme is redemption. Maybe the brother starts off on the wrong foot, or has been influenced by bad forces. The story then becomes about his journey to redeem himself and prove his worth to Goku and the others.
Power and training. Since Goku is known for his power - seeking, his brother in fanfics often has a similar drive. They might train in unique ways or discover new forms of power.
The theme of love against all odds is also quite prevalent. Given their different origins and the fact that Goku is already married in the original story, their relationship in fanfics has to overcome many obstacles. This could be social, moral or even physical (like dealing with other powerful characters who oppose their union), but they still find a way to be together, which makes for an interesting read.
Friendship and mentorship are also common. Goku is often seen as a mentor figure to Caulifla in these fanfics. They form a bond through training and fighting side by side. Another theme could be the exploration of different universes. Given that they are from different universes in the Dragon Ball series, fanfics may play around with the idea of them exploring each other's worlds and cultures.
One common theme is growth. Both caulifla and goku are Saiyans, so fanfics often focus on their growth in power, like learning new techniques.
Power and dominance are common themes. Since Goku Black was already a powerful character, in the female versions, the focus often remains on her strength and how she uses it to get what she wants.
The theme of power is also prevalent. Their combined power or the pursuit of greater power individually can be a central focus. Some fics might have them training to reach new levels of power, like achieving new Super Saiyan forms, which is very exciting to read about.
A common theme is rivalry - turned - friendship. Given their history in the original story, many fics explore how they can move past their animosity.
One common theme is the clash of their different cultures. Goku is from a more action - oriented, martial - arts based Saiyan culture, while Diana is from the Amazonian culture. Their interactions in fanfics often explore how these two very different cultures can coexist or influence each other.
Adventure is a big theme as well. Given Goku's love for fighting and exploring, and Mera's own adventurous spirit in some interpretations, they embark on all sorts of quests in fanfics. They could be searching for a lost artifact or trying to stop an evil force from taking over a particular realm.
Common themes include the father - son relationship. This is explored in different ways like Goku's absence at times and how it affects Gohan and then how they reconnect. Another is the exploration of Gohan's potential. Goku is usually there to unlock that potential. There are also themes related to the Saiyan culture. How Goku passes on knowledge about their race to Gohan and how Gohan uses that knowledge in battles and in life.
One common theme is redemption. Frieza is often portrayed as having a chance at redemption through his interactions with Goku. For example, in some fanfics, Goku's unwavering belief in the good in people (or in Frieza's case, beings) starts to make Frieza question his own evil ways.