Find all functions $f ,g,h : R\to R$ such that $f(x+y^3)+g(x^3+y) = h(xy)$ for all $x,y \in R$ 

To find all functions \( f, g, h : \mathbb{R} \to \mathbb{R} \) such that \( f(x+y^3) + g(x^3+y) = h(xy) \) for all \( x, y \in \mathbb{R} \), we can proceed as follows:

1. **Substitute specific values for \( x \) and \( y \)**:
   - Let \( x = 0 \):
     \[
     f(y^3) + g(y) = h(0)
     \]
   - Let \( y = 0 \):
     \[
     f(x) + g(x^3) = h(0)
     \]

2. **Analyze the equations obtained**:
   - From \( f(y^3) + g(y) = h(0) \), we can express \( g(y) \) in terms of \( f \):
     \[
     g(y) = h(0) - f(y^3)
     \]
   - From \( f(x) + g(x^3) = h(0) \), we can express \( g(x^3) \) in terms of \( f \):
     \[
     g(x^3) = h(0) - f(x)
     \]

3. **Equate the two expressions for \( g \)**:
   - Since \( g(y) = h(0) - f(y^3) \) and \( g(x^3) = h(0) - f(x) \), we have:
     \[
     h(0) - f(y^3) = h(0) - f(x)
     \]
   - This implies:
     \[
     f(y^3) = f(x)
     \]

4. **Consider the implications of \( f(y^3) = f(x) \)**:
   - For \( f(y^3) = f(x) \) to hold for all \( x, y \in \mathbb{R} \), \( f \) must be a constant function. Let \( f(x) = c \) for some constant \( c \).

5. **Substitute \( f(x) = c \) back into the original equations**:
   - If \( f(x) = c \), then:
     \[
     c + g(y) = h(0)
     \]
     \[
     c + g(x^3) = h(0)
     \]
   - This implies \( g(y) = h(0) - c \) and \( g(x^3) = h(0) - c \), so \( g \) must also be a constant function. Let \( g(x) = d \) for some constant \( d \).

6. **Determine the relationship between the constants**:
   - From \( c + d = h(0) \), we have:
     \[
     d = h(0) - c
     \]

7. **Substitute \( f(x) = c \) and \( g(x) = d \) into the original functional equation**:
   - The original equation becomes:
     \[
     c + d = h(xy)
     \]
   - Since \( c + d = h(0) \), we have:
     \[
     h(xy) = h(0)
     \]
   - This implies \( h \) must also be a constant function. Let \( h(x) = e \) for some constant \( e \).

8. **Verify the consistency of the constants**:
   - From \( c + d = e \) and \( d = h(0) - c \), we have:
     \[
     c + (h(0) - c) = h(0)
     \]
     \[
     e = h(0)
     \]

Thus, the only solutions are constant functions \( f(x) = c \), \( g(x) = h(0) - c \), and \( h(x) = h(0) \).

The final answer is \( \boxed{ f(x) = c } \), \( g(x) = h(0) - c \), and \( h(x) = h(0) \).