To simplify this expression, we can use the trigonometric identity:

1 + cot(a) = csc(a)

And

1 + tan(a) = sec(a)

Therefore, sin^3(a)csc(a) + cos^3(a)sec(a)

= sin^3(a)(1 + cot(a)) + cos^3(a)(1 + tan(a))

= sin^3(a)csc(a) + cos^3(a)sec(a)

= cos(a)sin^2(a) + sin(a)cos^2(a)

= sin(a)*cos(a)(sin(a) + cos(a))

= sin(2a)

Therefore, the simplified expression is sin(2a).