Selling non-primary residence - Gift of equity/cost basis and capital gains.

Purchased house four years ago from ailing mother. She owed $155k on the mortgage. I purchased the home by borrowing that amount and then assuming a gift of equity from my mother to bring the cost basis of the house to $267k, at the time, fair market value.

Four years later I am selling the home for $300k and after fees and such I expect to clear about $275k on the sale.

My question is about the taxable gains on the home as I will owe capital gains tax on the sale because I had not live there. Are the capital gains taxed on the $275k less $267k basis? Or would I be taxed on the gains from what I borrowed? $275k - $155k? 

In addition, I need to send half of these proceeds to my sibling as part of his entitlement to her estate. Can I gift the cash to my sibling under the same rules as the gift of equity from the home purchase - tax free?

Thank you