No. Strangely downpayments and loans are irrelevant to the gain calculation.
If you could deduct the downpayment from your gain consider what would happen if you sold it the next day for the same price you paid. There should be no gain right? You got what you paid. Sure you would need to use some of the proceeds to pay off the mortgage. If you got to deduct the downpayment you would have a $50k loss to offset other income. That doesn't make sense.
Your gain is about the purchase price and the sale price. Not whether you pay the seller with cash or borrowed money.
Here's another example. I buy a house for $250k. I put down $50k and borrow $200k.
Over the years I pay off $100k of the mortgage principal (more with interest of course) and then sell for $500k. I add a new deck for $10k at some point (maybe I can increase the rent after that.) Also over the year's I have taken $30k in depreciation. What is my gain?
Gain = net proceeds of sale minus adjusted basis
Adjusted basis = original cost + capital improvements (additions, etc.) - depreciation allowed or allowable
So in my example your adjusted basis is $250k + 10k (new deck) - $30k (depreciation) = $230k
My gain is $500k - $230k = $280k.
You can see the downpayment and mortgage payoff doesn't matter TO TAXES. However it matters to what you put in your pocket.
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