"Mansions" is hard to quantify; whether a given house was a mansion will be subjective, and doesn't correlate super well with the amount of financial support they gave their child. But if you want to really dig into the details:
> Gates
His father was a high powered lawyer in Seattle; his mother was a member on a number of corporate and philanthropic boards, including one that gave her direct access to the Chairman of IBM at the precise moment that Microsoft was attempting to sell software to IBM.
> Bezos
His parents loaned him a quarter million dollars to start Amazon in the mid 90s.
> Ballmer
His father was a "manager" at Ford, which could mean a wide range of things; he grew up in a very wealthy area.
> Allen
He seems to have come from genuinely middle class roots - his parents were a librarian and an elementary school teacher.
> Musk
This one is pretty complicated; his father owned an emerald mine and seems to have been quite wealthy, though Elon disputes his father's claim that he invested money in Elon's first company.
> Page
Both parents were academics in computer science.
> Brin
Both parents were academics, immigrating from the USSR to the US - his father ended up teaching math at the University of Maryland, his mother doing research at NASA.
So that's two (Gates and Bezos) where their parents were significantly wealthy and influential in useful ways; two where it's unclear how much they got real benefit from their parents' wealth, but they certainly didn't grow up poor (Ballmer and Musk); two where the parents weren't rich but academically involved (Page and Brin); and one where they were genuinely just middle class folks (Allen).
> Gates
His father was a high powered lawyer in Seattle; his mother was a member on a number of corporate and philanthropic boards, including one that gave her direct access to the Chairman of IBM at the precise moment that Microsoft was attempting to sell software to IBM.
> Bezos
His parents loaned him a quarter million dollars to start Amazon in the mid 90s.
> Ballmer
His father was a "manager" at Ford, which could mean a wide range of things; he grew up in a very wealthy area.
> Allen
He seems to have come from genuinely middle class roots - his parents were a librarian and an elementary school teacher.
> Musk
This one is pretty complicated; his father owned an emerald mine and seems to have been quite wealthy, though Elon disputes his father's claim that he invested money in Elon's first company.
> Page
Both parents were academics in computer science.
> Brin
Both parents were academics, immigrating from the USSR to the US - his father ended up teaching math at the University of Maryland, his mother doing research at NASA.
So that's two (Gates and Bezos) where their parents were significantly wealthy and influential in useful ways; two where it's unclear how much they got real benefit from their parents' wealth, but they certainly didn't grow up poor (Ballmer and Musk); two where the parents weren't rich but academically involved (Page and Brin); and one where they were genuinely just middle class folks (Allen).