Social Security benefits are not earned income, but that doesn't matter. The tax on long-term capital gain has nothing to do with earned income. Earned income is not the same as ordinary income. For calculating the tax on long-term capital gain, everything except qualified dividends and long-term capital gain is treated the same and is taxed as ordinary income. It doesn't matter whether it's earned income or unearned income. Earned income and unearned income are lumped together and treated the same.
You have left out several items of information that affect how much of your long-term capital gain will be taxed at each rate. One missing item is your filing status. I will assume, as I did earlier, that you are filing as single. Another missing item is your date of birth. The fact that you are getting Social Security benefits raises the possibility that you were 65 or older as of the end of 2020. Your age matters because you get a larger standard deduction if you are 65 or older, and that reduces your taxable income. Another missing item is whether you are blind, which would also increase your standard deduction. I am assuming you are not blind. Finally, I am assuming that you are using the standard deduction, not itemized deductions, and that you have no deductions or adjustments to income other than the standard deduction.
Not all of your Social Security is included in your income. The amount that is included depends on your other income. With the new figures you have given, 85% of your Social Security, or $22,950, would be included in your income. So the total income on your tax return would be $78,950 ($22,950 plus the $56,000 long-term capital gain).
Please note that all of the following is based on 2020 tax rates.
If you are single, under 65, and not blind, your standard deduction is $12,400, so your taxable income is $66,550 ($78,950 total income minus $12,400 standard deduction). That is $26,550 over the $40,000 top of the 0% bracket, so $26,550 of your long-term capital gain would be taxed at the 15% rate.
If you are single, 65 or older, and not blind, your standard deduction is $14,050, so your taxable income is $64,900 ($78,950 total income minus $14,050 standard deduction). That is $24,900 over the $40,000 top of the 0% bracket, so $24,900 of your long-term capital gain would be taxed at the 15% rate.
