formula for multinomial expansion raised to three

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who could kindly give me the formula for $$(x_1+x_2 + \cdots+ x_n) ^3,$$ in the form like the case $$(x_1+x_2 + \cdots+ x_n) ^2 = \sum^n_{i=1} x_i^2 + 2\sum_{1\leq i<j\leq n} x_ix_j.$$

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$$\sum_i x_i^3+3\sum_{i\neq j}x_i^2 x_j+6\sum_{\substack{\{i,j,k\}\\i\neq j\neq k}}x_ix_jx_k$$