Representation of integers by a family of cubic forms

Under certain conditions on the coefficients, we derive asymptotic formulas for the number of representations of zero and of large positive integers by the cubic forms that can be written as $L_{1}(x_{1},x_{2},x_{3}) Q_{1}(x_{1},x_{2},x_{3})+ L_{2}(x_{4},x_{5},x_{6}) Q_{2}(x_{4},x_{5}, x_{6}) + a_{7} x_{7}^{3}$ , where L ₁ and L ₂ are linear forms, Q ₁ and Q ₂ are quadratic forms, and a ₇ is a nonzero integer.