Coin change problem : UVa 11137 - Ingenuous Cubrency

Hey, I have just started learning Dynamic Programming. I solve the problem in this way.

for(i=0;i<21;i++)
        for(j=0;j<N;j++)
            if(j>=coins[i])
                ways[j]+=ways[j-coins[i]];

then I try to solve By recursion. The below code gives me AC.

int makecube ;
i64 dp[22][10000] ;
i64 arr[22];
i64 rec( i64 i , i64 total )
{

    if( i >= 21 ) {
        if( total == makecube ) {
            return 1 ;
        } else return 0 ;
    }

    if( dp[i][total] != -1 )return dp[i][total] ;

    i64 ret1 = 0;
    i64 ret2 = 0 ;
    if( total + arr[i] <= makecube )ret1 = rec( i , total + arr[i] ) ;
    ret2 = rec( i+1 , total ) ;

    return dp[i][total] = ret1 + ret2 ;

}

int main()
{
    for( int i = 1 ; i <= 21 ; i++  )arr[i-1] = i*i*i ;
    while( SI( makecube ) == 1 ) {
        mem( dp , -1 ) ;
        printf("%lld\n",rec( 0 , 0 )) ;
    }

    return 0;
}

And finally I tried to code like this,

int makecube ;
int arr[] = { 0 , 1 ,  8 ,  27 ,  64 ,  125 ,  216 ,  343 ,  512 ,  729 ,  1000 ,  1331 ,  1728 ,  2197 ,  2744 ,  3375 ,  4096 ,  4913 ,  5832 ,  6859 ,  8000 ,  9261 } ;
i64 dp[21][10000] ;

i64 rec( i64 i , i64 total )
{
    if( total == makecube ) {
        return 1 ;
    }
    if( i == 22 ) {
        return 0 ;
    }

    if( dp[i][total] != -1 )return dp[i][total] ;

    i64 ret1 = 0;

    for( int j = 1 ;total+j*arr[i] <= makecube ; j++ ) {
        ret1 += rec( i+1 , total + j*arr[i] );
    }
    return dp[i][total] = ret1 ;

}

int main()
{
    while( SI( makecube ) == 1 ) {
        mem( dp , -1 ) ;
        printf("%lld\n",rec( 1 , 0 )) ;
    }

    return 0;
}

Can anyone please find what is problem for the second recursive solution. This solution even do not give ans for given test cases.