It isn’t the force but the energy that causes mass.
If you compress a spring and that spring now contains the potential energy that was used to compress that spring, the spring has more mass. Surprising as it may seem – a compressed spring has more mass than the same spring uncompressed although that difference will be so small as to be hard to measure unless it is a huge spring.
So energy whether potential or kinetic results in mass (the famous Einstein equation) That could be from gravity potential, kinetic energy due to motion etc. Not only the strong force.
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