I assume you are looking for an InterpolationOrder option. Below is an example from the documentation that shows how it works even for a 6x6 data grid.
data = Table[Sin[j^2 + i], {i, 0, Pi, Pi/5}, {j, 0, Pi, Pi/5}]; Table[ListDensityPlot[data, Mesh -> None, InterpolationOrder -> o, ColorFunction -> "SouthwestColors"], {o, {0, 1, 2, 3}}]

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