Key idea. Express the required quantities using the known sum and product.

1. Expand the square of the sum:

   \[(x+y)^2=x^2+2xy+y^2.\]

   So \(x^2+y^2=7^2-2\cdot10=29\).

2. For the cubes, expand \((x+y)(x^2-xy+y^2)\). The mixed terms cancel, leaving \(x^3+y^3\).

3. Therefore

   \[x^3+y^3=(x+y)(x^2+y^2-xy)=7(29-10)=133.\]

Remember. Find an identity that uses what you know; solving for the individual numbers may be unnecessary.