In this question, we are given that the cost of gold varies directly as the cube of its weight. This means that if the weight of gold piece increases by a certain factor, the cost will increase by the cube of that factor.

We are also given that a gold piece weighing 20 decigram costs ?1,000. Let`s denote the cost of the gold piece as C and the weight as W. According to the given information, we can write the equation C = k * W^3, where k is a constant of proportionality.

We want to find the profit or loss incurred when the gold piece is broken into two pieces whose weights are in the ratio 2:3. Let the weights of the two pieces be W1 and W2, where W1/W2 = 2/3.

Since the cost varies directly with the cube of the weight, the ratio of the costs should also be the cube of the weight ratio. Let the cost of the first piece be C1 and the cost of the second piece be C2.

We have C1/C2 = (W1/W2)^3 = (2/3)^3 = 8/27.

Now, let`s substitute the equation C = k * W^3