Are there any production function $f(x_1,\ldots,x_n)$ that is having decreasing returns to scale, given that the marginal product in every input $i$ in the function $f$ is constant?
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Seems like the only function $f$ that fits your description $$ \forall i: \frac{\partial f(\mathbf{x})}{\partial x_i} = c_i $$ is $$ f(\mathbf{x}) = A + \sum x_i c_i. $$ (Frequently $f(\mathbf{0}) = 0$ is assumed. The assumption is referred to as "no free lunch".)
Then you can apply the definition of returns to scale.
