Yes. Up to 85% of your Social Security benefits can be taxable. There is no age limit for having to pay taxes on Social Security benefits if you have other sources of income along with the SS benefits. When you have other income such as earnings from continuing to work, investment income, pensions, etc. up to 85% of your SS can be taxable.
What confuses people about this is that before you reach full retirement age, if you continue working while drawing SS, your benefits can be reduced if you earn over a certain limit. (For 2016 that limit was $15,720) After full retirement age, no matter how much you continue to earn, your benefits are not reduced by your earnings; your employer will still have to withhold for Social Security and Medicare.