Key idea. Recognise both terms as perfect cubes.

1. Write \(8a^3=(2a)^3\) and \(27b^3=(3b)^3\).

2. The sum-of-cubes factorisation is

   \[u^3+v^3=(u+v)(u^2-uv+v^2).\]

3. Substitute \(u=2a\), \(v=3b\):

   \[8a^3+27b^3=(2a+3b)(4a^2-6ab+9b^2).\]

Remember. In the quadratic factor for a sum of cubes, the middle sign is negative.