The song "Someday", where Sonic vows that someday he will unite with his siblings.
Manic's song, "Home", where he finally feels like he belongs in the idyllic Mobodoon.
Then, at episode's end, he realizes his real home is with his brother and sister.
Mindy's song, "Money Can't Buy," wherein she states that money can't buy what she really needs.
"Let the Children Light the Way" from "Tangled Webs."
Queen Aleena saving the hedgehogs at times, showing how much she cares for her kids.
"Have You Got the 411?" has a verse where Sonic sings about how he'll do anything to see his mom again.
The hedgehogs being adopted by their foster parents; special mention goes to Manic, who was stolen from his doorstep... but then Farrel sees he's a baby. Nobody would have been surprised if Farrel had just dumped him on another doorstep, or even thrown him out with the trash, but he raises Manic as his foster son.
Although the parental figures for each sibling were vastly different, each tried their best to raise them given their knowledge and circumstances. For instance, Farrel imparts everything he knows about thievery to Manic, so that Manic will have a means to live when he grows up. Because each sibling grew up with attentive and loving adoptive parents, it means that their childhoods weren't necessarily bad ones in spite of the absence of their birth mother.
At the end of the first episode, Sonia cries that with her foster mother gone, she doesn't have a home anymore, but Manic and Sonic say she does in them.
The bond between Sonic, Sonia, and Manic is this pretty much all the time; despite their snarking at each other, the hedgehogs deeply care for one another.
The hedgehogs helping the good Robotnik and redeeming their evil counterparts in the mirror universe episode.