A cryogenic substance is found to have a specific heat capacity \(c\) that varies with temperature according to \(c=\beta T^{2}\), where \(\beta\) is an empirically derived constant with units \(\mathrm{J} / \mathrm{K}^{3} \cdot \mathrm{kg}\). If \(231 \mathrm{~J}\) of energy must be transferred thermally to an \(8000-\mathrm{mg}\) sample of this substance to raise the temperature of the sample from 1. 00 to \(6.00 \mathrm{~K}\), what is the value of \(\beta\) ?