Let \(X\) be a smooth projective connected curve of genus \(g\geq 1\) defined over \(\bar{\mathbb{Q}}\), and let \((J,\lambda)\) denote the Jacobian of \(X\), endowed with its canonical principal polarization. For a given divisor \(\alpha\) of degree one on \(X\) and for an \(r\)-tuple of non-zero integers \(m=(m_1,\cdots,m_r)\) with \(0\leq r\leq g\), \(d=\sum_{i=1}^rm_i\), let \(Z_{m,\alpha}\) denote the image of the map \(X^r\rightarrow J\) defined by \((x_1,\cdots, x_r)\mapsto \sum_{i=1}^rm_ix_i-d\alpha\). The main aim in this paper is to develop a method to calculate the Néron-Tate heights \(\text{h}'_{\mathcal{L}}(Z_{m,\alpha})\). The author alaborates on Zhang’s method in [S.-W. Zhang, Invent. Math. 179, No. 1, 1–73 (2010; Zbl 1193.14031)] that allows to compute the height of the Gross-Schoen cycle. More precisely, he shows the following: Assume that \(g\geq 2\). Then there exist rational numbers \(a,b,c\) depending only on \(m\) and \(g\) such that for all number fields \(k\), all smooth projective geometrically connected curves \(X\) of genus \(g\) with semistable reduction over \(k\), and all \(\alpha\in\text{Div}^1X\) the equality \(\text{h}'_{\mathcal{L}}(Z_{m,\alpha})=\frac{1}{[k:\mathbb{Q}]}\left(a\langle\hat{\omega},\hat{\omega}\rangle+b\sum_{vin M(k)}\varphi(X_v)\text{log}Nv\right)+c\text{h}'_{\mathcal{L}}(\alpha-(1/(2g-2)K_X\) holds, where \(M(k)\) denotes the set of places of \(k\).