Energy of a graph is defined as the sum of the absolute values of the eigenvalues of the adjacency matrix associated with the graph. In this research work, we find color energy, distance energy, Laplacian energy, and Seidel energy for the Dutch windmill graph of cycle lengths 4, 5, and 6. Also, we find the lower bounds of the double-wheel graph for energy, Seidel energy, color energy, distance energy, Laplacian energy, and Harary energy.