An entrepreneurial Miami family is building a thriving business based on one son’s fixation on socks and their other son’s tireless sales work.

A weakness of many corporate leaders is a reluctance to delegate. Not so with Sebastian Martinez, CEO of Miami-based sock company Are You Kidding. For him delegating begins on his business card. Between “phone” and the number it reads “Call my mom.”

Sebastian, 9, and his brother, Brandon, 12, director of sales (he prefers to be called the D.O.S) are the front men in a fast-growing family business they both readily acknowledge their mom, Rachel Martinez, 38, founded and guides. With some prompting they will mention their self-effacing dad, Fabian Martinez, 40, helps with the heavy lifting.

“Our dad is basically the dinner person, he’s the chef, and he’s the heavyweight dude,’’ said Brandon, who like his brother, categorized his parents in part by the meals they prepare. Both brothers extolled their mom’s breakfast cooking.

Are You Kidding was founded on Sebastian’s preoccupation with socks from earliest childhood but relies on the business and marketing savvy Rachel accrued during a 12-year career selling advertising in Latin America for Televisa, the huge Mexican media company. She got the idea for a sock company after watching a TV show featuring Maddie Robinson, who began designing beach sandals shaped like fish when she was just 8.

“I looked at Sebastian and asked him if he wanted to design socks, because he just loves socks,’’…