Another theme is the power of teamwork. Since they all have unique abilities, when they combine their powers, they can achieve great things. In some fanfictions, they face an enemy that is too strong for any one of them alone, but together they are able to defeat it. This shows how important it is for them to cooperate. It also emphasizes their individual growth within the team, like Shadow learning to be more open and Amy becoming more confident in her abilities while Sonic sharpens his leadership skills.
Love triangles can also be a theme, although not always in a romantic sense. Sometimes it's about the love for their world or their friends. For instance, Amy's love for Sonic might be compared to her loyalty to her friends, including Shadow. And Shadow's sense of duty to protect the world can be seen as a form of love, which then gets intertwined with Sonic and Amy's own motives and relationships.
One common theme is friendship. Despite their different personalities, Sonic, Amy, and Shadow often have to learn to be friends and work together. For example, in many fanfictions, they start off not getting along but end up relying on each other.