(1) 求 $7{\mathrm{C}}_6^3-4{\mathrm{C}}_7^4$ 的值;

(2) 设 $m,n\in {\mathbf{N}}^{*},n⩾m$, 求证:

$(m+1)C_m^m+(m+2)C_{m+1}^m+(m+3)C_{m+2}^m+\cdots +n{C}_{n-1}^m+(n+1)C_n^m=(m+1)C_{n+2}^{m+2}$